Soliton molecules and few-cycle-pulse solitons structures for the generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation

Jia, Man

doi:10.1007/s11071-023-08899-5

Cited by 5 publications

(1 citation statement)

References 41 publications

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“…Based on this mechanism, soliton molecules have been discovered in several famous integrable systems [22][23][24][25][26][27][28][29], including the complex modified KdV equation [22], the (2 +1)-dimensional bidirectional Sawada-Kotera system [23], and the Sharma-Tasso-Olver-Burgers system [24]. In addition, dromion molecules described by the variable separation solution were reported for the first time by applying the multilinear variable separation approach to the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli system [29].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal symmetries, soliton-cnoidal wave solution and soliton molecules to a (2+1)-dimensional modified KdV system

Wang,

Ren

2024

Commun. Theor. Phys.

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A (2+1)-dimensional modified KdV (2DmKdV) system is considered from several perspectives. Firstly, residue symmetry, a type of nonlocal symmetry, and the B"{a}cklund transformation are obtained via the truncated Painlev'{e} expansion method. Subsequently, the residue symmetry is localized to a Lie point symmetry of a prolonged system, from which the finite transformation group is derived. Secondly, the integrability of the 2DmKdV system is examined under the sense of consistent tanh expansion solvability. Simultaneously, explicit soliton-cnoidal wave solutions are provided. Finally, abundant patterns of soliton molecules are presented by imposing the velocity resonance condition on the multiple-soliton solution.

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