On the Lie symmetries of the boundary value problems for differential and difference sine-Gordon equations

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YILDIRIM Ö., Caglak S.

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, vol.102, no.2, pp.142-153, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 102 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.31489/2021m2/142-153
  • Journal Name: BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.142-153
  • Keywords: symmetry analysis, partial differential equations, difference equations, boundary value problems
  • Yıldız Technical University Affiliated: Yes

Abstract

In general, due to the nature of the Lie group theory, symmetry analysis is applied to single equations rather than boundary value problems. In this paper boundary value problems for the sine-Gordon equations under the group of Lie point symmetries are obtained in both differential and difference forms. The invariance conditions for the boundary value problems and their solutions are obtained. The invariant discretization of the difference problem corresponding to the boundary value problem for sine-Gordon equation is studied. In the differential case an unbounded domain is considered and in the difference case a lattice with points lying in the plane and stretching in all directions with no boundaries is considered.