10,885 papers in this slice of arXiv.
Hiroshi Noguchi
Nonequilibrium membrane pattern formation is studied using meshless membrane simulation. Bound proteins are considered to have two states that generate different membrane spontaneous curvatures. Protein binding and unbinding occur cyclically owing to chemical potential differences, as an off-lattice active Potts model. It is found that this cyclic binding/unbinding can induce blinking domains, with oscillating size: convex domains of the proteins with a higher spontaneous curvature grow, and subsequently, the proteins change to the other state with a lower spontaneous curvature, resulting in domain shrinkage. These processes repeat. In thermal equilibrium, hexagonal convex domains are formed by the competition between bending and surface tension energies, so that they are stably formed only under positive surface tension. However, blinking domains can form even in tensionless membranes.
C. Senthil Kumar, R. Radha
In this paper, we travel through an unknown territory of dromions, to unearth and show the new properties/attributes of dromions which have never been brought to the fore since they were first discovered by Boiti etal [1]. These new attributes are brought out by investigating a generalized (2+1) dimensional Nonlinear Schrodinger (NLS) equation by exploiting Truncated Painleve approach. The signatures that can be attributed to dromions include existence of firewall and reflection at the boundary, uneven distribution of energy among different bound states, amplitude dependence on adjacent dromions, etc. We have corroborated the main analytical results with numerical simulations also. We categorically state that these properties are universal and can be extracted in any (2+1) dimensional nonlinear partial differential equation. We do believe that these properties which shed more light on the behaviour of dromions may have wider repercussions in nonlinear optics, Bose-Einstein condensates and plasma physics.
Naresh Saha, Nirmoy Kumar Das, Ashoke Das +1
In this article, the nonlinear Helmholtz equation with non-Kerr nonlinearity, such as self steepening and self frequency shift, is considered. A travelling wave transformation is applied, and the extended nonlinear Helmholtz equation is reduced to a Hamiltonian dynamical system. Then, the reduced Hamiltonian system is analyzed by classification of equilibrium points, phase space analysis, and the construction of exact wave solutions. The relationship between the reduced dynamical coefficients and the original physical parameters is further established through a parameter space analysis. It is shown that self steepening directly modifies the reduced dynamics, whereas self frequency shift acts through the compatibility condition for the real travelling wave reduction. Together, these non-Kerr effects reshape the phase space geometry and travelling wave structure. Localized and periodic travelling waves are obtained, with their existence determined by the balance among dispersion, nonparaxiality, Kerr nonlinearity, and non-Kerr effects. Furthermore, a periodically forced version of the reduced system is examined to study the transition from regular to irregular dynamics. It has been observed that external forcing can induce complex oscillatory behavior. Bifurcation analysis, time series evolution, phase space analysis, largest Lyapunov exponent, and Poincaré section demonstrate the emergence of quasiperiodic and chaotic responses under sufficiently strong forcing. All analytical branches are verified through full-equation residual evaluation, while a few selected branches are additionally examined through direct numerical propagation and robustness tests under complex Gaussian perturbations. The results show that self steepening directly renormalizes the effective nonlinear dynamics, whereas self frequency shift restricts the admissible real-envelope travelling wave manifold.
Dmitry A. Zezyulin
We present quasistationary ring-shaped soliton necklaces in a two-component envelope propagating in a medium with competing cubic-quintic nonlinearity. Metastable propagation of soliton necklaces results from a balance of repulsion between adjacent out-of-phase solitons in one component and confinement by the boundary of a flattop region in the other. Numerical simulations demonstrate metastable propagation over about a hundred diffraction lengths, even with random noise added to the input envelopes. The maximum number of solitons in metastable necklaces can be controlled either by changing the size of individual solitons or by adjusting the width of the flattop region hosting the necklace.
Manuel A. Martínez Sánchez, Christoph Adam, Danial Saadatmand
We investigate the collision dynamics of two bright sphalerons in a (1+1)-dimensional deformed φ6 scalar field theory with a symmetric potential possessing false vacua. Two one-parameter realizations of the model, referred to as the barrier and well models, are considered and their static and linear instability properties are first reviewed. We then study head-on collisions of boosted sphalerons over a broad range of initial velocities and deformation parameters. The scattering dynamics exhibit a rich variety of final states, including the production of kink-antikink pairs, long-lived oscillons in true and false vacuum, multiple oscillons propagating in false-vacuum regions, and radiative decay. A particularly remarkable outcome is the emergence of a long-lived bubble of the false broken vacuum bounded by a kink-antikink pair, which repeatedly collapses and re-expands before eventually decaying into an oscillon. These results demonstrate that deformed φ6 theories with false vacua exhibit considerably richer sphaleron dynamics than previously known and provide new insight into the role of unstable localized configurations in nonlinear field theories.
Denis Mujo, Dušan Vudragović, Paulsamy Muruganandam +1
In this paper we present Open Multi-Processing (OpenMP) Fortran 90/95 programs to solve the Gross-Pitaevskii equation for a rotating dipolar Bose-Einstein condensate (BEC) in two and three dimensions, which is a new version of our previous published programs for a dipolar Bose-Einstein condensate without rotation. After the recent experimental study of a rotating dipolar BEC [L. Klaus et al., Nature Phys. 18, 1453 (2022)], the present programs will be useful tools for related theoretical investigation. The algorithm used is the split-step semi-implicit Crank-Nicolson scheme for imaginary- and real-time propagation to obtain stationary states and BEC dynamics, respectively, as in the previous version [L. E. Young-S. et al., Comput. Phys. Commun. 286 (2023) 108669].
Yuchen He, Amin Chabchoub, Zhan Wang
While conventional rogue wave statistical models rely on linear or weakly nonlinear descriptions of random seas, we demonstrate experimentally that moderately or strongly nonlinear wave fields can be represented by sparse ensembles of coherent soliton-like packets. These packets exhibit log-normal amplitude distributions together with uniformly distributed phases and peak emergence times. This sparse coherent structure framework naturally leads to an extreme value description in which the probability of exceedance is governed by the tail of the coherent-structure amplitude distribution. The prediction is validated against laboratory hydrodynamic experiments across a variety of unidirectional sea states, showing good agreement with the experimental observations and comparing favourably with conventional statistical prediction models while retaining analytical simplicity. Our results provide a direct physics-based link between sparse coherent structures and rogue wave probabilities, with broader implications for nonlinear wave physics in optics, cold gases, and plasmas.
Nguyen Duc Anh Quan, Do Duc Tho, Marek Trippenbach +3
Four-wave mixing provides a simple setting in which dispersion, nonlinearity, and non-Hermiticity compete to select resonant energy-transfer channels. We study degenerate four-wave mixing in a Kerr dual-core coupler with balanced gain and loss and frequency-dependent intercore coupling. The dispersive coupling changes the symmetry from conventional PT symmetry to a combined CPT symmetry and reshapes the two-branch linear spectrum. We determine the unbroken-CPT domain and classify the branch configurations that can satisfy the degenerate phase-matching condition. In the parameter ranges examined, three resonant channels persist over broad regions, whereas a same-branch channel appears only close to the symmetry-breaking threshold. In this near-threshold regime, a single pump can simultaneously satisfy two distinct nonzero sideband resonances. Direct pulse simulations confirm the predicted resonances and reveal secondary-wave generation and multifrequency cascades near eigenmode coalescence. A reduced three-wave model captures the initial dynamics away from the exceptional point but loses accuracy as the modal basis becomes ill-conditioned. These results show how dispersive coupling reorganizes resonances, group-velocity mismatch, and nonlinear energy exchange in a non-Hermitian wave system, and they identify the exceptional-point region as a regime where a few-mode description can break down.
Nguyen Duc Anh Quan, Le Xuan The Tai, Doan Quang Tri +3
We investigate two parity-time-symmetric ring resonators coupled over a finite angular region described by a super-Gaussian profile. In the linear regime, analytical spectra are obtained in the homogeneous-coupling and fixed-amplitude narrow-contact limits, while the finite-width problem is treated numerically. Local coupling introduces nonzero spatial Fourier components that mix angular harmonics and lift the degeneracy of counterpropagating modes, resolving each excited doublet into parity-dependent branches. Collisions among these branches generate multiple exceptional-point boundaries and disconnected broken-PT domains. The resulting phase diagrams exhibit re-entrant unbroken-broken-unbroken transitions when the gain-loss strength, coupling width, or peak coupling amplitude is varied. The numerical spectra continuously recover both analytical limits. In the nonlinear regime, selected ground and excited linear modes are used as seeds for adiabatic propagation into finite-amplitude Kerr waveforms that remain dynamically persistent over the simulated observation interval for finite ranges of nonlinear strength. These results show that the spatial profile of inter-resonator coupling provides a geometric means of controlling multimode PT transitions and selecting dynamically accessible nonlinear waveforms in coupled-ring systems.
Merlin Pelz
Two identical scalar dynamical systems coupled through a scalar diffusion equation are studied herein, with respect to bifurcations from a symmetric steady-state to symmetric and asymmetric steady-states and to in-phase and anti-phase oscillations. Numerical continuations based on the developed theory show the shape of the bifurcation branches and the attracting nonlinear states far from bifurcation onset and confirm their, for the most part, derived stability. This study extends the work on the dynamical properties of a single scalar dynamical system coupled to its own delay through an adjacent diffusion field and quantifies further the delay of diffusive information transmission between two such Wentzell boundaries. The mathematical system is motivated by modeling biological membranes with yet unknown effective local fluxes that are coupled to bulk diffusion.
David D. J. M. Snee, Yi-Ping Ma
We report nonlinear edge waves in a 2D mechanical topological insulator. A bulk lattice consists of pendulums with on-site cubic nonlinearity connected by linear springs realizing quantum spin Hall effect. We show that the nonlinear interaction between two edge modes with equal group velocities (EGV) is described by a 1D two-component coupled nonlinear Schrödinger (CNLS) equation. On the interface separating two bulk lattices with opposite spin Chern numbers, we construct linear springs such that the dispersion relation exhibits EGV points with favorable CNLS coefficients. Thus, we realize nonlinear edge waves propagating along the interface, including bright-bright (BB) edge solitons for focusing CNLS coefficients, and dark-dark edge solitons, edge domain walls, and dark-bright edge solitons for defocusing CNLS coefficients. In terms of the site amplitudes, these solutions resemble bright and dark breathers. These solutions should be topologically protected when both carrier frequencies lie within a band gap, which we explicitly show by passing BB edge solitons through compact defects on the interface. We also show energy transfer in BB edge soliton collisions with potential application to collision-based computing. Generally, vector edge solitons exhibit a large parameter space for soliton collisions, which endows mechanical devices with greater potential for information processing and other functionalities.
Chengbo Zhang, Xiaohui Gao
We investigate pseudovorticity generation in Gaussian beams undergoing self-focusing under amplitude and phase noise, using the cubic-quintic nonlinear Schrödinger equation. Pseudovorticity, defined as the curl of the optical momentum flux, characterizes local rotational flow in the absence of phase singularities. Our numerical simulations show that thermal amplitude and phase noise induce a multipolar pseudovorticity pattern. Unlike the pure cubic case, where noise asymmetries are radiated away during collapse, the quintic saturation arrests collapse and traps the noise in the resulting soliton. Hence, pseudovorticity multipoles persist, oscillating at the focusing-refocusing period. These results suggest a potential pathway for controlling local optical torque through noise engineering.
Nikolaos K. Efremidis, Demetrios N. Christodoulides
Whereas conventional Gaussian focusing gradually concentrates optical energy around the focal plane, abruptly autofocusing waves maintain a low peak intensity over most of their evolution before undergoing a sudden, high-contrast intensity surge at a prescribed focus. Since their introduction in 2010, their two-dimensional spatial realizations have enabled applications ranging from particle manipulation and material processing to terahertz generation and nonlinear optics. The recent work of Cao et al. marks the transition from (2+1)-dimensional spatial autofocusing to the full space-time domain through the experimental synthesis of spherical Airy wavepackets. This advance opens new opportunities for ultrafast structured light, tightly localized energy delivery, and nonlinear photonics.
C. M. Schober, A. Islas
We extend the Carter-Govan multiple-scales analysis of weakly viscous, narrowband deep-water wave packets beyond Dysthe order within the potential-flow reduction of Dias, Dyachenko, and Zakharov (DDZ). We seek to determine whether this framework generates the complex multiplier (1+iβ) used phenomenologically to modify the nonlocal Dysthe mean-flow interaction. Although order counting places a direct viscous carrier-mean interaction at sixth order, it does not exclude an indirect fifth-order contribution arising from viscosity dependent lower-order harmonics and nonlinear interactions. We therefore derive the first correction to the induced mean flow and the complete fifth-order first-harmonic solvability condition. The resulting nonlocal terms are derivative--dependent and contain no explicit viscosity, excluding the proposed indirect mechanism within the DDZ framework. At sixth order, a restricted calculation of the nonlinear viscous block isolates a direct carrier-mean contribution with the same operator structure as the imaginary component of the prescribed mean-flow correction. Independently, a finite-adjustment-time model yields an exact, frequency dependent mean-flow response. Its low-frequency expansion produces the multiplier 1+iβeff(Ω), with βeff(Ω)=Ωτ. When Ωτ=O(ε), the resulting phase-lag correction enters at fifth order, one order beyond the leading Dysthe mean-flow interaction.
Shiva Kumar
Analytical expressions for the phase variance in a nonlinear fiber optic system based on phase-shift keying are developed. The Gauss-Hermite functions are used as the orthogonal basis to represent the noise field. Number of degrees of freedom (DOF) to accurately model the phase variance is estimated. The amplifier noise excites higher order Gauss-Hermite noise modes and the nonlinear mixing of a signal pulse and higher order Gauss-Hermite noise mode leads to new noise fields which enhance the nonlinear phase noise. The higher order noise modes propagate linearly and enhance the linear phase noise if the matched filter is not used at the receiver. Analytical expression for the optimum launch power is developed taking into account the linear and nonlinear phase noise.
Avner Peleg, Debananda Chakraborty
We present the first demonstration of transition to spatiotemporal chaos with multiple colliding pulse sequences in systems described by perturbed cubic nonlinear Schrödinger (NLS) equations. For this purpose, we consider propagation of multiple sequences of optical pulses in two distinct types of nonlinear waveguide arrays with cubic gain and loss. By employing a perturbation theory for NLS solitons, we show that the dynamics of pulse energies in the waveguide array systems is described by generalized Lotka-Volterra (LV) models, which exhibit dissipative chaos in a wide region in parameter space. We test the LV models' predictions for chaotic dynamics of pulse energies by extensive numerical simulations with perturbed systems of coupled-NLS equations. We find excellent agreement between the results of the LV and coupled-NLS models for energy dynamics in both types of waveguide array systems, despite the strong pulse pattern distortions and the strongly nonlinear nature of the dynamics.
Marko. M. Ćosić, Andrew N. Jordan
We investigate the quantum interference and energetic phenomena associated with classical caustics in the quantum bouncing ball problem, we refer to as quantum caustics. By considering an initial Gaussian wavepacket, we show that caustics associated with the underlying classical trajectory families are exhibited. We connect the associated phase singularity chains in the vicinity of the caustic with the semiclassical Pearcey function built on the cusp catastrophe lines. We also quantify the amount of superenergy exhibited in these solutions - regions of space where the local energy exceeds the largest constituent energy eigenvalue. We give a complimentary description of the caustic and superenergy behavior using the Madelung/Bohm trajectories, which gives additional insight about the energy of the trajectories and how they traverse the phase singularity chains.
Wang Fa-Ren, Jia Man, Lou S Y
The deformation algorithm based on conservation laws can lift (1+1)-dimensional integrable systems to higher-dimensional counterparts while preserving Lax integrability, yet its generalization to (2+1)-dimensional models has remained an open problem. This paper establishes a unified deformation framework for two (2+1)-dimensional integrable equations: the anisotropic Kadomtsev-Petviashvili (KP) equation and the isotropic Nizhnik-Novikov-Veselov (NNV) equation. By introducing a set of mutually commuting field-dependent deformation operators, we systematically construct infinite families of (m+3)-dimensional integrable KP and NNV hierarchies, derive their closed-form Lax pairs, and rigorously verify integrability via the vanishing commutator condition of Lax operators. For each high-dimensional hierarchy, concrete finite-dimensional master systems are obtained by truncating auxiliary spatial variables: a (3+1)-dimensional KP system and a (4+1)-dimensional generalized NNV system. Further symmetry reductions recover the original (2+1)-dimensional KP and NNV equations, and more importantly produce two distinct Harry-Dym (HD)-type reciprocal integrable systems. The KP reduction yields an anisotropic (2+1)-dimensional HD model, while the NNV reduction generates the first spatially isotropic two-space-dimensional HD system reported so far, filling a notable gap in existing literature. Parallel comparison of the KP and NNV branches reveals that the spatial symmetry of the original two-dimensional parent equation directly governs the symmetry properties of its high-dimensional deformations and HD dual subsystems. Our work not only extends the conservation-law deformation conjecture beyond (1+1)-dimensions to accommodate both strong Lax and weak Lax structures, but also provides a universal route to construct reciprocal links for multi-dimensional integrable systems.
Eugene Kogan
We solve exactly the inverse problem for traveling fronts in a lossy nonlinear transmission line. Starting from a prescribed hyperbolic-tangent profile, we determine the voltage--charge relation that supports it. In the general case, the solution is expressed in terms of the lower incomplete beta function, while for positive integer or half-integer values of the front-width parameter m, it reduces to elementary functions. We analyze the distinction between kinks and shocks and show that all physically admissible fronts obtained in the exact construction are shocks. We obtain an approximate solution for the inverse problem which gives the voltage--charge relation in terms of elementary functions (for any m). We also solve the direct problem and obtain the approximate hyperbolic-tangent shock profile for a prescribed cubic voltage--charge relation. In the inverse approach, the shock parameters may be prescribed independently, subject to the admissibility conditions, whereas in the direct approach they are determined by the prescribed voltage--charge relation. The exact and approximate inverse solutions agree through order m−2 in the broad-shock limit, and numerical comparisons show good agreement even outside this asymptotic regime.
Boris A. Malomed
This minireview provides a brief summary and a discussion of directions for further development of theoretical and, chiefly, experimental studies of bright solitons in optical couplers, i.e., dual-core waveguides which combine the linear inter-core coupling (tunneling of light between the parallel cores with the intra-core group-velocity dispersion and self-focusing Kerr (cubic) nonlinearity. Following a short introduction to the field, the article focuses on a brief review of relatively recent experimental results for the switching of solitons in dual-core nonlinear optical fibers and the spontaneous emergence of stable asymmetric two-core solitons in the couplers with the symmetric dual-core structure.