Kink Soliton Dynamic of the (2+1)-Dimensional Integro-Differential Jaulent–Miodek Equation via a Couple of Integration Techniques


Cakicioglu H., ÖZIŞIK M., SEÇER A., Bayram M.

Symmetry, vol.15, no.5, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 5
  • Publication Date: 2023
  • Doi Number: 10.3390/sym15051090
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: a sub-version of auxiliary equation method, energy-dependent Schrödinger potential, generalized Kudryashov method, Lie symmetry, smooth-kink soliton
  • Yıldız Technical University Affiliated: Yes

Abstract

In this article, the aim was to obtain kink soliton solutions of the (2+1)-dimensional integro-differential Jaulent–Miodek equation (IDJME), which is a prominent model related to energy-dependent Schrödinger potential and is used in fluid dynamics, condensed matter physics, optics and many engineering systems. The IDJME is created depending on the parameters and with constant coefficients, and two efficient methods, the generalized Kudryashov and a sub-version of an auxiliary equation method, were applied for the first time. Initially, the traveling wave transform, which comes from Lie symmetry infinitesimals (Formula presented.) and (Formula presented.), was applied, and a nonlinear ordinary differential equation (NODE) form was derived. In order to make physical interpretations, appropriate solution sets and soliton solutions were obtained by performing systematic operations in line with the algorithm of the proposed methods. Then, 3D, 2D and contour simulations were made. Interpretations of different kink soliton solutions were made by obtaining results that are consistent with previous studies in the literature. The obtained results contribute to the studies in this field, though the contribution is small.