A Regularized System for the Nonlinear Variational Wave Equation

TL;DR

This paper introduces a generalized nonlinear variational wave equation, proves the existence of smooth solutions locally in time, and shows how it reduces to the classical form in a special case.

Contribution

The paper presents a new generalized form of the nonlinear variational wave equation and establishes local existence of smooth solutions.

Findings

Existence of local smooth solutions for the generalized system

Recovery of the classical nonlinear variational wave equation as a limit

New theoretical framework for analyzing nonlinear wave equations

Abstract

We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.