On Stable Difference Schemes for the Solution of Soliton Type Coupled Sine-Gordon Equations in the Weak Sense

YILDIRIM Ö.

Advances in Applied Mathematics and Mechanics, vol.18, no.3, pp.988-1008, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 3
  • Publication Date: 2026
  • Doi Number: 10.4208/aamm.oa-2023-0049
  • Journal Name: Advances in Applied Mathematics and Mechanics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.988-1008
  • Keywords: Existence, finite difference method, uniqueness, weak solutions
  • Yıldız Technical University Affiliated: Yes

Abstract

In the present paper numerical solution of the nonlinear coupled system of sine-Gordon equations is studied in the weak sense. A first-order accurate and two second-order accurate unconditionally stable difference schemes corresponding to the system of sine-Gordon equations are considered. Solutions of these difference schemes are presented in the space of distributions by variational methods. The fixed point theory and the finite difference method are combined in the numerical implementations, carried out in MATLAB, in order to verify the theoretical results.