Soliton molecules and asymmetric solitons in three fifth order systems via velocity resonance

Abstract

Soliton molecules can be formed in some possible mechanisms both theoretically and experimentally. In this paper, we introduce a new mechanism, namely the velocity resonant, to find soliton molecules. Under the velocity resonance mechanism, two solitons can form a kink-antikink molecule, an asymmetric soliton, a two-peak soliton and/or a far away bounded molecule depended on the selections of the wave numbers and the distance between two solitons of a molecule. The results are exhibited via three well known fifth order integrable systems which serve as a general fluid model, as well as models many other physical fields.

Novel Soliton Molecules and Wave Interactions for A (3+1)-Dimensional Nonlinear Evolutionary Equation

“…It has been mathematically revealed that a soliton molecule can be generated from an exact two-soliton solution [25]. A new mechanism, the velocity resonant, has been proposed to find soliton molecules [26,27]. Hinted by this scheme, we have found interesting dromion molecules in a dromion lattice [12].…”

Characteristics of the Soliton Molecule and Lump Solution in the 2 + 1 -Dimensional Higher-Order Boussinesq Equation

“…The theoretical frameworks to address the soliton molecule have been introduced [18,19]. Recently, Lou proposed the velocity resonance mechanism to construct the soliton molecules of the ð1 + 1Þ-dimensional nonlinear systems [20]. The velocity resonance mechanism is one of the useful methods to form the soliton molecule [20].…”

“…Recently, Lou proposed the velocity resonance mechanism to construct the soliton molecules of the ð1 + 1Þ-dimensional nonlinear systems [20]. The velocity resonance mechanism is one of the useful methods to form the soliton molecule [20]. To balance the nonlinear effects, the high-order dispersive terms may play a key role in the velocity resonance mechanism [21].…”

Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

“…Recently, the hybrid solutions of lump solutions with other types of solutions draw a lot of attention, which include lump-soliton [17][18][19], lump-kink solution [20], resonance stripe solitons [21][22][23], and some hybrid solutions [24][25][26]. Very recently, Lou [27] introduced a new possible mechanism, the velocity resonant, to form soliton molecules and asymmetric solitons of three (1 + 1)-dimensional fluid models: fifth-order KdV, SK equation, and KK equation. To the best of our knowledge, soliton molecules interacting with lump waves and breather waves has not been studied yet.…”