ON DISCRETIZATION OF DARBOUX INTEGRABLE SYSTEMS ADMITTING SECOND-ORDER INTEGRALS

Zheltukhin K. , Zheltukhina N.

UFA MATHEMATICAL JOURNAL, vol.13, no.2, pp.170-186, 2021 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.13108/2021-13-2-170
  • Title of Journal : UFA MATHEMATICAL JOURNAL
  • Page Numbers: pp.170-186
  • Keywords: Darboux integrability, discretization, HYPERBOLIC-EQUATIONS

Abstract

We consider a discretization problem for hyperbolic Darboux integrable systems. In particular, we discretize continuous systems admitting x - and y-integrals of the first and second order. Such continuous systems were classified by Zhyber and Kostrigina. In the present paper, continuous systems are discretized with respect to one of continuous variables and the resulting semi-discrete system is required to be also Darboux integrable.