Lax representation and a quadratic rational first integral for second-order differential equations with cubic nonlinearity

Dmitry I. Sinelshchikov, Partha Guha, A. Ghose Choudhury

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper we give a Lax formulation for a family of non-autonomous second-order differential equations of the type yzz+a3(z,y)yz3+a2(z,y)yz2+a1(z,y)yz+a0(z,y)=0. We obtain a sufficient condition for the existence of a Lax representation with a certain L-matrix. We demonstrate that equations with this Lax representation possess a quadratic rational first integral. We illustrate our construction with an example of the Rayleigh–Duffing–Van der Pol oscillator with quadratic damping.

Original languageBritish English
Article number106553
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume112
DOIs
StatePublished - Sep 2022

Keywords

  • Cubic second-order differential equations
  • Lax representation
  • Rational first integrals

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