General Solution to Unidimensional Hamilton-Jacobi Equation

Abstract

A method for finding the general solution to the partial differential equations: \ $F(u_x,u_y)=0$; \ $F(f(x)u_x,u_y)=0$ \ (or \ $F(u_x,h(y)u_y)=0$) \ 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: \ $F(f(x)u_x,u_y)=G(x)$, and then applied to unidimensional Hamilton-Jacobi equation.

Accepted for presentation at ICIAM 2011 - 7th International Congresson Industrial and Applied Mathematics 2011 in Vancouver, BC, Canada

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• Comment to "General Solution to Unidimensional Hamilton-Jacobi Equation" [arXiv:1302.0591v1]