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Novel Soliton Molecules, Periodic Wave and other Diverse Wave Solutions to the New (2 + 1)-Dimensional Shallow Water Wave Equation

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Abstract

In this research, we focus on some novel exact solutions of the new (2 + 1)-dimensional shallow water wave equation (SWWE). First, the soliton molecules on the (x,y)-, (x,t)- and (y,t)-planes are constructed via assigning the velocity resonance conditions to the multiple soliton solutions (MSSs) that can be derived via the Hirota method. Second, the periodic wave solutions are explored by means of the new homoclinic approach. Finally, the other diverse wave solutions including the kink wave, singular wave and the singular periodic wave solutions are also plumbed by the sub-equation approach (SEA). The dynamic performances of the extracted solutions are presented graphically to unveil the nonlinear physical characteristics. As we know, the extracted solutions in this paper are all new and have not been investigated in other literature, which can help us make sense of the nonlinear dynamics of the new (2 + 1)-dimensional SWWE better.

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Data Availability

No datasets were generated or analysed during the current study.

Abbreviations

SWWE:

Shallow water wave equation

MSSs:

Multiple soliton solutions

SM:

Soliton molecules

VRCs:

Velocity resonance conditions

PWSs:

Periodic wave solutions

SEA:

Sub-equation approach

NHA:

New homoclinic approach

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Funding

This work was supported by the Key Programs of Universities in Henan Province of China (22A140006), Program of Henan Polytechnic University (B2018-40).

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Authors and Affiliations

  1. School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo, 454003, China

    Kang-Jia Wang, Shuai Li, Feng Shi & Peng Xu

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  1. Kang-Jia Wang
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  2. Shuai Li
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Material preparation, data collection and analysis were performed by Kang-Jia Wang. The draft of the manuscript was written by Kang-Jia Wang and Peng Xu. Software by Shuai Li and Feng Shi.

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Correspondence to Peng Xu.

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Wang, KJ., Li, S., Shi, F. et al. Novel Soliton Molecules, Periodic Wave and other Diverse Wave Solutions to the New (2 + 1)-Dimensional Shallow Water Wave Equation. Int J Theor Phys 63, 53 (2024). https://doi.org/10.1007/s10773-024-05577-z

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