Study of the N-soliton Solution for the (2 + 1)-dimensional Generalized Bogoyavlensky-Konopelchenko Equations
Wuming Li *
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo City, 454003, Henan Province, China.
Ai Jing
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo City, 454003, Henan Province, China.
*Author to whom correspondence should be addressed.
Abstract
This paper presents a systematic investigation of the N-soliton solutions for the (2+1) -dimensional generalized Bogoyavlensky-Konopelchenko equation. By employing the Hirota bilinear method, we have rigorously derived the analytical expressions of the N-soliton solutions. Using the Maple software, various three-dimensional structural patterns and corresponding density distribution plots are generated. Furthermore, the interaction evolution behaviors of soliton solutions are also graphically illustrated by selecting different time values, providing visual representations of the dynamical process of soliton solutions. It is demonstrated well that the studied equation has various special interaction patterns between different soliton types, such as interaction solutions between line and periodic solitons; kink periodic and kink solitons; line and lump solitons; lump and kink solitons; two periodic solitons; two kink periodic solitons, and so on. Numerical simulations indicated that all these interactions exhibit the characteristics of elastic collisions. This study offers valuable insights into the soliton behaviors that occur in integrable systems, including nonlinear physics, fluid mechanics, and optical fiber communication, among others.
Keywords: (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation, Line Soliton, kink soliton, periodic soliton, lump soliton