Soliton molecules and novel smooth positons for the complex modified KdV equation

Soliton Molecules and Full Symmetry Groups to the KdV-Sawada-Kotera-Ramani Equation

“…It is usually not easy to derive a soliton molecule containing multiple solitons. In order to obtain a soliton molecule containing multiple solitons, one can investigate N-solitons from Darboux transform to find a soliton molecule with multiple solitons [14]. The method to construct soliton molecules and the symmetry group method can be applied to investigate other nonlinear models.…”

“…In 2019, Lou [11] introduced a velocity resonant mechanism to form soliton molecules and asymmetric solitons for three-fifth order systems. Very recently, soliton molecules and some hybrid solutions involving Lump, breather, and positon have been investigated for some (1 + 1)-dimensional and (2 + 1)-dimensional equations by Hirota bilinear method and Darboux transformation [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

“…The fission and fusion of the solitary waves are all the resonance phenomena [18][19][20]. Soliton molecules are the bound states of solitons which have been experimentally discovered on optical systems [21][22][23]. Soliton molecule is essentially a velocity resonance soliton [24][25][26].…”

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

“…To balance the nonlinear effects, the high-order dispersive terms may play a key role in the velocity resonance mechanism [21]. The soliton molecule of a variety of integrable systems has been verified with the velocity resonance mechanism: the fifth-order Korteweg-de Vries (KdV) equation [22,23], the modified KdV equation [24,25], the ð3 + 1Þ -dimensional Boiti-Leon-Manna-Pempinelli equation [26], and so on [27]. The dynamics between soliton molecules and breather solutions and between soliton molecules and dromions are presented by the velocity resonance mechanism, the Darboux transformation, and the variable separation approach [25][26][27][28].…”