Degeneration of N-soliton solutions for a (3+1)-dimensional nonlinear model in shallow water waves

With the support of bilinear method, specific N -soliton solutions of a ( 3 + 1 )-dimensional nonlinear model are proposed, and various solutions are constructed through the different degeneration processes of N -soliton solutions. On the basis of defining a novel constraint condition on N -soliton...

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Published inNonlinear dynamics Vol. 111; no. 2; pp. 1667 - 1683
Main Authors Li, Longxing, Dai, Zhengde, Cheng, Bitao
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.01.2023
Springer Nature B.V
Subjects
Automotive Engineering
Breathers
Classical Mechanics
Control
Degeneration
Dynamical Systems
Engineering
Mathematical models
Mathematics
Mechanical Engineering
Original Paper
Shallow water
Solitary waves
Vibration
Water waves
Resonance
Hirota–Satsuma–Ito equation
High-order lumps
Interaction solutions
High-order breathers
type solitons
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Summary:With the support of bilinear method, specific N -soliton solutions of a ( 3 + 1 )-dimensional nonlinear model are proposed, and various solutions are constructed through the different degeneration processes of N -soliton solutions. On the basis of defining a novel constraint condition on N -soliton solutions, resonance Y -type solitons are found out. Under complex conjugating method (complexification method), N -soliton solutions could convert to high-order breathers ( T -order breathers). Resorting to long wave limit technique, high-order lumps ( M -order lumps) are obtained. During the partial degeneration of N -soliton solutions, combining complexification method and long wave limit technique, abundant interaction solutions composed of soliton, breather and lump are yielded. The corresponding numerical simulations are presented to demonstrate the dynamic behaviors of the obtained solutions.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-022-07911-8