A New Nonlinear Equation with Lump‐Soliton, Lump‐Periodic, and Lump‐Periodic‐Soliton Solutions

Abstract

An extended (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff-like equation is proposed by using the generalized bilinear operators based on a prime number p=3. By combining multiexponential functions with a quadratic function, the interaction between lumps and multikink soliton is generated. In the meanwhile, the interaction of lump with periodic waves and the interaction among lumps, periodic waves, and multikink soliton can be obtained by introducing the ansätz forms. The dynamics of these interaction solutions are analyzed graphically by selecting appropriate parameters.

Lump and Mixed Rogue‐Soliton Solutions of the (2 + 1)‐Dimensional Mel’nikov System

“…where a 1 k 1 ≠ 0 and a 9 > 0. e interaction solutions between two bright solitons and a rogue wave are shown in Figure 6 with the parameters selected as m 1 � 1, m 2 � 3, k 1 � 0.8, a 1 � − 3.2, a 4 � 2, and Figure 6: e propagations of the interaction solutions between two bright solitons and rogue wave (2) with (15) and (16) taking the parameters Complexity a 8 � 1. Figure 6 represents the spatial structures of propagation for this interaction solution of two bright solitons with a rogue wave at different times t � − 30, − 5, 0, 5, 30, respectively.…”

“…Many methods are very powerful to investigate the nonlinear evolution equations, such as the Darboux transformation [2,6], the inverse scattering transformation [1,7], and the Hirota bilinear method [8,9]. Recently, lump waves, rogue waves, and the interaction solutions between the lump and soliton have intensively aroused much attention [10][11][12][13][14][15][16][17].…”

Solitons, Rogues and Interaction Behaviors of Third-Order Nonlinear Schrodinger Equation

“…Sometimes these massive rogue waves will become tsunamis, due to underwater disturbance such as earthquakes, volcanic eruptions, typically with the aid of nuclear explosion or asteroids 10 . There are many powerful methods proposed for rogue wave solution, such as the Hirota bilinear method [12][13][14][15][16][17][18][19][20][21][22][23] , the Darboux transformation 24,25 and the extended homoclinic test method 26 . To describe complex physical phenomena, the interactions between multi-solitons and rogue waves are getting more attention.…”

Investigating One-, Two-, and Triple-Wave Solutions via Multiple Exp-Function Method Arising in Engineering Sciences

“…(ii) The extended (2 + 1)-dimensional Calogero-Bogoyavlenskii-Schiff (eCBS) equation [35] is given as…”

“…The eCBS equation will be changed to a (2 + 1)-dimensional CBS equation when δ 1 = δ 2 = δ 3 = 0 [36]. Ren et al [35] investigated the extended (2 + 1)-dimensional Calogero-Bogoyavlenskii-Schiff-like equation by using the generalized bilinear operators based on a prime number p = 3.…”