A study of Bogoyavlenskii’s (2+1)-dimensional breaking soliton equation: Lie symmetry, dynamical behaviors and closed-form solutions

Results in Physics

Hassan Almusawa¹  Shubham Kumar Dhiman²  Sachin Kumar³  M.S. Osman³  Amit Kumar⁴ 

[1] Corresponding author.;Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia;Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India;Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt;

关键词: Bogoyavlenskii’s breaking soliton equation;    Lie symmetry reductions;    Soliton solutions;    Infinitesimal generators;    Exact closed-form solutions;   

DOI  :  

来源: DOAJ

【 摘 要 】

This paper employs the Lie symmetry analysis to investigate novel closed-form solutions to a (2+1)-dimensional Bogoyavlenskii’s breaking soliton equation. This Lie symmetry technique, used in combination with Maple’s symbolic computation system, demonstrates that the Lie infinitesimals are dependent on five arbitrary parameters and two independent arbitrary functions f1(t)and f2(t). The invariance criteria of Lie group analysis are used to construct all infinitesimal vectors, commutative relations of their examined vectors, a one-dimensional optimal system and then several symmetry reductions. Subsequently, Bogoyavlenskii’s breaking soliton (BBS) equation is reduced into several nonlinear ODEs by employing desirable Lie symmetry reductions through optimal system. Explicit exact solutions in terms of arbitrary independent functions and other constants are obtained as a result of solving the nonlinear ODEs. These established results are entirely new and dissimilar from the previous findings in the literature. The physical behaviors of the gained solutions illustrate the dynamical wave structures of multiple solitons, curved-shaped wave–wave interaction profiles, oscillating periodic solitary waves, doubly-solitons, kink-type waves, W-shaped solitons, and novel solitary waves solutions through 3D plots by selecting the suitable values for arbitrary functional parameters and free parameters based on numerical simulation. Eventually, the derived results verify the efficiency, trustworthiness, and credibility of the considered method.

【 授权许可】

Unknown