A note on exact results for Burgers-like equations involving Laguerre derivatives

TL;DR

This paper explores exact solutions for Burgers-like and KdV-like equations involving Laguerre derivatives, extending solution methods to nonlinear and variable coefficient cases, and establishing a general scheme for such equations.

Contribution

It introduces a general scheme for constructing exact solutions to Burgers-like equations with Laguerre derivatives, including nonlinear and variable coefficient cases.

Findings

Exact solutions constructed using separation of variables.

Extension to nonlinear time-fractional equations.

Solutions for Burgers and KdV-like equations with Laguerre derivatives.

Abstract

In this note, we consider some Burgers-like equations involving Laguerre derivatives and demonstrate that it is possible to construct specific exact solutions using separation of variables. We prove that a general scheme exists for constructing exact solutions for these Burgers-like equations, extending to more general cases, including nonlinear time-fractional equations. Exact solutions can also be obtained for KdV-like equations involving Laguerre derivatives. We finally consider a particular class of Burgers equations with variable coefficients whose solution can be obtained similarly.