Exact Travelling Wave Solutions of Some Nonlinear Nonlocal Evolutionary Equations

TL;DR

This paper applies an algebraic method to find exact solutions, including kink-like and soliton-like forms, for various nonlinear nonlocal evolutionary equations such as the nonlinear telegraph and nonlocal hydrodynamic models.

Contribution

It introduces a direct algebraic approach to derive exact solutions for complex nonlinear nonlocal PDEs, focusing on special solution types.

Findings

Exact kink-like solutions constructed for the equations.

Soliton-like solutions obtained and analyzed.

Method demonstrated on multiple nonlocal PDEs.

Abstract

Direct algebraic method of obtaining exact solutions to nonlinear PDE's is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some spatially nonlocal hydrodynamic-type model. Special attention is paid to the construction of the kink-like and soliton-like solutions.