Painleve analysis of travelling wave solutions and analysis of energy estimates for a nonlinear Sobolev-type equation

A. I. Aristov<sup>abc

a</sup> Lomonosov Moscow State University, Moscow, 119991 Russia Federal Research Center “Computer Sciences and Control”, Russian Academy of Sciences, Moscow, 119333 Russia MIREA -- Russian Technological University, Moscow, 119454 Russia
^b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
^c MIREA — Russian Technological University, Moscow

Abstract: There is considerable interest in studying unbounded solutions of nonlinear partial equations. In many cases, energy estimates can be used to prove that the solution tends to infinity in finite time, while also providing an estimate for the latter. Here, an equation in which energy estimates fail to gauge the cases when solutions exhibit such behavior was analyzed. A class of unbounded solutions was explored using the Painleve analysis.

Keywords: nonlinear partial equation, Sobolev-type equation, Painleve analysis, Laurent series.

UDC: 517

Received: 20.08.2023
Accepted: 14.09.2023

DOI: 10.26907/2541-7746.2023.3.182-189