Dynamics of nonlinear dark waves and multi-dark wave interactions for a new extended (3+1)-dimensional Kadomtsev–Petviashvili equation

Zhong, Jie; Tian, Lin; Wang, Binji; Ma, Zhimin

doi:10.1007/s11071-023-08784-1

Cited by 7 publications

(1 citation statement)

References 45 publications

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“…Compared to existing classical methods, BNNM is able to obtain error-free exact analytical solutions of the equations by constructing some single layer or deep layer activation functions, instead of numerical solutions with errors. Due to the universality of BNNM, many rich solutions can be obtained, such as, bright and dark solitons [22], breather solutions [23], periodic solution [24], rogue wave solution [25], interference wave solution [26], M-lump waves [27,28], multi-wave solution [29], interaction solutions [30], traveling wave solution [31], soliton-type solutions [32]. Thus BNNM outperforms the Hirota bilinear method in terms of constructing and accurately fitting the original function, among others.…”

Section: Introductionmentioning

confidence: 99%

Lump waves, bright-dark solitons and some novel interaction solutions in (3+1)-dimensional shallow water wave equation

Lei,

Tian,

2024

Phys. Scr.

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The (3+1)-dimensional Geng equation is an extended version of the KdV model that describes the wave dynamics behavior of shallow water waves in complex applications. In this study, we discuss the (3+1) dimensional Geng equation using the bilinear neural network method. By incorporating specific activation functions into the neural network model, new test functions are constructed. Using symbolic computational techniques and selecting appropriate parameters, we systematically obtain new meaningful exact solutions of some (3+1)-dimensional Geng equations, including dark lump solutions, three kinds of interaction solutions, and bright and dark soliton solutions. Furthermore, the results are visualized through diagrams of different categories, which intuitively demonstrate the evolution process and physical characteristics of the waves.

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