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Novel soliton dynamics and IMEX-DG scheme for the Kuramoto–Tsuzuki model

Author

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  • Maurya, Devraj
  • Singh, Ajeet
  • Jiwari, Ram
  • Pandit, Sapna

Abstract

Herein, the authors derived new soliton-type analytical solutions of the Kuramoto-Tsuzuki (KT) model via tanh-coth method and then numerically simulate the model by interior penalty discontinuous Galerkin (IPDG) scheme. In the development of numerical scheme, IPDG and implicit–explicit (IMEX) Euler techniques used for space and time discretization. This work’s main innovation is the derivation of a boundedness lemma via a Lyapunov functional, which has never been done before for issues of this kind in the DG environment. We created precise a priori error estimates of the completely discrete scheme using this boundedness criterion. The Lyapunov-based estimations, which naturally extend to the nonlinear context, guarantee the scheme’s stability. Next, we prove that our proposed method achieve optimal convergence rates theoretically as well as numerically for both spatial and temporal discretizations in both L2-norm and DG norm.

Suggested Citation

  • Maurya, Devraj & Singh, Ajeet & Jiwari, Ram & Pandit, Sapna, 2026. "Novel soliton dynamics and IMEX-DG scheme for the Kuramoto–Tsuzuki model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 250(C), pages 1111-1127.
    • Handle: RePEc:eee:matcom:v:250:y:2026:i:c:p:1111-1127
    DOI: 10.1016/j.matcom.2026.07.040
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