Multiple soliton solutions and fusion interaction phenomena for the (2+1)-dimensional modified dispersive water-wave system

Diversity soliton excitations for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation

“…(3) Cross-like fractal soliton If we let: Localized solutions might be helpful to the propagation processes for non-linear waves in (2+1)-D equations. Peakons are some types of weak solutions of the (2+1)-D equations, and there is a finite discontinuity of the first derivative in the wave peak [22,23]. respectively, a fusion phenomenon between three peakons will be found, see fig.…”

Periodic oscillating solitons and homoclinic breather-wave solution for the (3+1)-dimensional Jimbo-Miwa equation

“…The high amplitude wave produced during the collision between soliton and breather can be used to elaborate the generation mechanism of rouge wave [2]. Multi-soliton or solitary wave solutions of non-linear PDE may well describe various phenomena in physics and other fields [3][4][5][6]. Some oscillating solitons may be considered as a kind of non-propagation solitons [7][8][9][10].…”

Consistent Riccati expansion for finding interaction solutions of (2+1)‐dimensional modified dispersive water‐wave system

“…In 2009, we obtained exact complex wave solutions for system () by using the projective Riccati equation expansion . In 2013, Wen et al constructed multiple soliton solutions with arbitrary functions for system () . In those papers, authors only obtained the soliton‐soliton interaction solutions.…”