General Solution to Unidimensional Hamilton-Jacobi Equation · arXivDesk
1302.0591Feb 4, 2013Accepted for presentation at ICIAM 2011 - 7th International Congresson Industrial and Applied Mathematics 2011 in Vancouver, BC, Canada
General Solution to Unidimensional Hamilton-Jacobi Equation
A method for finding the general solution to the partial differential equations: \ F(ux,uy)=0; \ F(f(x)ux,uy)=0
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\ (or \
F(ux,h(y)uy)=0
) \ is presented, founded on a Legendre like transformation and a theorem for Pfaffian differential forms. As the solution obtained depends on an arbitrary function, then it is a general solution. As an extension of the method it is obtained a general solution to PDE: \
F(f(x)ux,uy)=G(x)
, and then applied to unidimensional Hamilton-Jacobi equation.