Lie vector fields, conservation laws, bifurcation analysis, and Jacobi elliptic solutions to the Zakharov–Kuznetsov modified equal-width equation

Hosseini K., Alizadeh F., Sadri K., Hinçal E., AKBULUT A., Alshehri H., ...More

Optical and Quantum Electronics, vol.56, no.4, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.1007/s11082-023-06086-9
  • Journal Name: Optical and Quantum Electronics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, Civil Engineering Abstracts
  • Keywords: Bifurcation analysis, Conservation laws, Jacobi elliptic solutions, Lie symmetries, ZK–MEW equation
  • Bursa Uludag University Affiliated: Yes

Abstract

The present paper intends to thoroughly study an evolutionary model called the Zakharov–Kuznetsov modified equal-width (ZK–MEW) equation. More precisely, Lie symmetries as well as invariant solutions to the ZK–MEW equation describing shallow and stratified waves in nonlinear LC circuits are first derived, and then a general theorem established by Ibragimov is adopted to retrieve its conservation laws. Additionally, by applying the qualitative theory of dynamical systems, the bifurcation analysis of the dynamical system is carried out and several Jacobi elliptic solutions to the ZK–MEW equation are formally constructed. In some case studies, the impact of the nonlinear coefficient on the physical features of bright and kink solitary waves as well as periodic continuous waves is examined in detail.