General Solution to Unidimensional Hamilton-Jacobi Equation
Abstract
A method for finding the general solution to the partial differential equations: \ F(ux,uy)=0; \ F(f(x)\:ux,uy)=0 \ (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.
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