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<p>In this article, several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation method. Firstly we will investigate space-time fractional coupled Boussinesq-Burger dynamical model, which is used to model the propagation of water waves in shallow sea and harbor, and has many applications in ocean engineering. Secondly, we will investigate the space-time fractional coupled Drinfeld-Sokolov-Wilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal seabed. Thirdly, we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a dam. We obtained different solutions in terms of trigonometric, hyperbolic, exponential and Jacobi elliptic functions. Furthermore, graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction, periodic soliton, bright and dark solitons, Kink and anti-Kink solitons, breather-type waves and so on, which have applications in ocean engineering, fluid mechanics and other related fields. We hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.</p>

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Breathers and multi wave solutions of three different space-time fractional nonlinear coupled waves dynamical models and their applications

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • Ambreen Sarwar,
  • Tao Gang,
  • Muhammad Arshad,
  • Iftikhar Ahmed,
  • Dian-chen Lu

摘要

In this article, several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation method. Firstly we will investigate space-time fractional coupled Boussinesq-Burger dynamical model, which is used to model the propagation of water waves in shallow sea and harbor, and has many applications in ocean engineering. Secondly, we will investigate the space-time fractional coupled Drinfeld-Sokolov-Wilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal seabed. Thirdly, we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a dam. We obtained different solutions in terms of trigonometric, hyperbolic, exponential and Jacobi elliptic functions. Furthermore, graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction, periodic soliton, bright and dark solitons, Kink and anti-Kink solitons, breather-type waves and so on, which have applications in ocean engineering, fluid mechanics and other related fields. We hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.