New analytical wave structures for some nonlinear dynamical models via mathematical technique
Keywords:
Solitons; exp(−Φ(η))-expansion method, Yu-Toda-Sasa-Fukuyama model; (2 1)-dimensional nonlinear evolution equation, Water wave propagation with surface tension, hyperbolic solitary wave solutionAbstract
In this paper, we used Yu-Toda-Sasa-Fukuyama (YTSF) model, the (2 + 1)-dimensional nonlinear evolution equation, and water wave propagation with surface tension to find new traveling wave solutions by applying exp(??(?))expansion method (EEM). The proposed nonlinear wave models are essential in coastal and offshore studies to understand wave propagation, wave transformation, and coastal processes. They also play a crucial role in cryptography, the regulation of heartbeats, and mathematical physics. We generate 3D, 2D, and contour plots of discovered solutions by selecting suitable values for arbitrary parameters within the accurate range space. Hyperbolic, trigonometric, and exponential functions are used to express the resulting traveling wave solutions. The received solutions included dark, bright, periodic, kink, singular, bell-type, hyperbolic solitary wave solutions, and many more. By changing model parameters, it is possible to change the dynamics of the solutions that the model generates. These results highlight the complexity and nonlinear behavior of the system, indicating the need for further analysis and providing valuable insights for understanding and modeling similar physical systems. This work breaks new ground by utilizing the EEM to uncover solitonic solutions for an unsolved model, pushing the boundaries of the existing literature by introducing a new mathematical technique for addressing fractional nonlinear physical models. The proposed method is brief, clear, and trustworthy, resulting in fewer calculations and broad application.
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