Abstract
By N -soliton solutions and a velocity resonance mechanism, soliton molecules are constructed for the KdV-Sawada-Kotera-Ramani (KSKR) equation, which is used to simulate the resonances of solitons in one-dimensional space. An asymmetric soliton can be formed by adjusting the distance between two solitons of soliton molecule to small enough. The interactions among multiple soliton molecules for the equation are elastic. Then, full symmetry group is derived for the KSKR equation by the symmetry group direct method. From the full symmetry group, a general group invariant solution can be obtained from a known solution.
Highlights
Soliton molecules, known as multisoliton complexes, are the bound states of solitons which exhibit molecule-like behavior [1]
Investigation on soliton molecules provides a direct route to study the interactions between solitary waves, and the formation and dissociation of soliton molecules are closely related to subjects such as soliton collision, soliton splashing, soliton rains, and the trapping of solitons
From the full symmetry group, a general group invariant solution can be obtained from a known solution
Summary
Known as multisoliton complexes, are the bound states of solitons which exhibit molecule-like behavior [1]. Investigation on soliton molecules provides a direct route to study the interactions between solitary waves, and the formation and dissociation of soliton molecules are closely related to subjects such as soliton collision, soliton splashing, soliton rains, and the trapping of solitons. We will investigate the following KdVSawada-Kotera-Ramani equation [32,33,34]: ut. [36], the authors investigated Lie symmetries, exact solutions, and integrability to the KdV-Sawada-Kotera-Ramani equation.
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