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

TL;DR

This paper reviews previous results and methods for solving the multidimensional Hamilton-Jacobi equation, providing insights into the general solution techniques used in this area of mathematical physics.

Contribution

It summarizes existing solutions and methods for the multidimensional Hamilton-Jacobi equation, clarifying the approaches used to find the general solution.

Findings

Overview of previous results on the general solution

Description of methods used to derive solutions

Clarification of solution structures in multidimensional cases

Abstract

We present previous results on the general solution of the multidimensional Hamilton-Jacobi equation $\frac{\partial u}{\partial t} - \frac{\partial u}{\partial x_a} \frac{\partial u}{\partial x_a}= 0$ and methods that were used to find such general solution.