Multisoliton solutions, completely elastic collisions and non-elastic fusion phenomena of two PDEs

Abstract

A direct rational exponential scheme is introduced and applied to construct exact multisoliton solutions of the clannish random walker's parabolic and the Vakhnenko–Parkes equations. We discuss the nature of soliton solutions before and after their interactions, and present their fusion (non-elastic) and elastic collisions of the soliton solutions. These soliton solutions of the equations are connected to physical phenomena: weakly non-linear surface, internal waves in a rotating ocean and interacting population motions. In addition, some three-dimensional and contour plots of the soliton wave solutions are presented to visualize the dynamics of the models.

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