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

Abstract

Soliton molecules of the (2 + 1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived by N-soliton solutions and a new velocity resonance condition. Moreover, soliton molecules can become asymmetric solitons when the distance between two solitons of the molecule is small enough. Finally, we obtained some novel types of hybrid solutions which are components of soliton molecules, lump waves, and breather waves by applying velocity resonance, module resonance of wave number, and long wave limit method. Some figures are presented to demonstrate clearly dynamics features of these solutions.

Line Soliton Interactions for Shallow Ocean Waves and Novel Solutions with Peakon, Ring, Conical, Columnar, and Lump Structures Based on Fractional KP Equation

“…In order to better understand the conformable fractional derivatives and integrals, this paper also attempts to give a physical explanation of the conformable fractional derivative from the perspective of variable acceleration. Extending fractional calculus to other important topics of nonlinear integrable systems is worth studying, such as soliton molecules [30], full reversal symmetric multiple soliton solutions [31], financial rogue wave [32], long-time asymptotic behavior [33], initial-boundary value problems [34], and high-dimensional hierarchies of evolution equations and their Hamiltonian structures [35].…”

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

“…For the complex KSKR equation, the symmetry group is divied into five sectors which correspond to five values of σ in Eq. (15). At the same time, we can derive the classical Lie symmetry from Theorem 1 by taking arbitrary constants fc, ξ 0 , τ 0 g as some special infinitesimal parameter forms.…”

“…with ( 14) and (15). It is necessary to point out that when two-soliton solution (17) exhibits one soliton molecule structure, the velocity resonance condition is the same as (5).…”

“…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].…”

Lie Symmetry Analysis, Exact Solutions, and Conservation Laws of Variable-Coefficients Boiti-Leon-Pempinelli Equation

“…With the rapid development of research fields like hydrodynamics and quantum physics, it has become increasingly important to investigate the exact solutions and certain properties of nonlinear evolution equations [3][4][5]. Compared with the PDEs with constant coefficients, the PDEs with variable coefficients can describe richer natural phenomena and construct more detailed and complex physical models [6][7][8].…”