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The Riemann-Bäcklund method to a quasiperiodic wave solvable generalized variable coefficient $$(2+1)$$-dimensional KdV equation. (English) Zbl 1373.37165
Summary: In this paper, the Riemann-Bäcklund method is extended to a generalized variable coefficient $$(2+1)$$-dimensional Korteweg-de Vries equation. The soliton and quasiperiodic wave solutions are investigated systematically. The relations between the quasiperiodic wave solutions and the soliton solutions are rigorously established by a limiting procedure. It is proved that the periodic wave solutions tend to the soliton solutions under a small amplitude limit. Furthermore, the propagation characteristics of the soliton solutions and periodic wave solutions are discussed through the graphical analysis.

##### MSC:
 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35Q53 KdV equations (Korteweg-de Vries equations) 35C08 Soliton solutions 34C25 Periodic solutions to ordinary differential equations 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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