Pseudo-Exponential-Type Solutions of Wave Equations Depending on Several Variables

TL;DR

This paper develops explicit pseudo-exponential solutions for various linear and nonlinear wave equations involving multiple variables, using matrix identities to extend solution methods.

Contribution

It introduces a novel approach to construct explicit solutions for multi-variable wave equations via matrix identities, applicable to both linear and nonlinear cases.

Findings

Explicit solutions for Dirac, Loewner, and Schrödinger equations depending on two variables.

Solutions for nonlinear wave equations depending on three variables.

Method extends the class of solvable multi-variable wave equations.

Abstract

Using matrix identities, we construct explicit pseudo-exponential-type solutions of linear Dirac, Loewner and Schr\"odinger equations depending on two variables and of nonlinear wave equations depending on three variables.