Eikonal 2.0: General Solutions for Modified Eikonal Equations

TL;DR

This paper derives implicit general solutions and analyzes symmetries for a class of modified eikonal equations, expanding the understanding of their mathematical structure and solution space.

Contribution

It introduces a method to find implicit solutions and explores symmetries for modified eikonal equations, which were not previously well-understood.

Findings

Derived implicit general solutions for modified eikonal equations

Analyzed symmetries of these equations

Expanded the theoretical understanding of solution structures

Abstract

We find implicit general solutions for modified eikonal equations $u_a u_a=F(u_t)$, where lower indices at dependent variables designate derivatives, $a=1,2,..,n$, and summation is implied over the repeated indices. We will consider the general solutions and symmetries of these equations.