New type of rogue waves

Ustinov, N.V.

doi:10.1016/j.chaos.2024.114467

Chaos, Solitons & Fractals

2024

DOI: 10.1016/j.chaos.2024.114467

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New type of rogue waves

N.V. Ustinov

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2024

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Cited by 4 publications

References 45 publications

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Dynamical analysis of solitons, breathers and periodic rogue waves for the variable-coefficient fourth-order nonlinear Schrödinger equation

Song,

Liu,

Wen

et al. 2024

Nonlinear Dyn

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Dynamical analysis of solitons, breathers and periodic rogue waves for the variable-coefficient fourth-order nonlinear Schrödinger equation

Song,

Liu,

Wen

et al. 2024

Nonlinear Dyn

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Double-pole dark-bright mixed solitons for a three-wave-resonant-interaction system

Wu,

Gao

2024

Applied Mathematics Letters

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Interactions of localized wave and dynamics analysis in the new generalized stochastic fractional potential-KdV equation

Zhu,

Huang,

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we investigate the new generalized stochastic fractional potential-Korteweg–de Vries equation, which describes nonlinear optical solitons and photon propagation in circuits and multicomponent plasmas. Inspired by Kolmogorov–Arnold network and our earlier work, we enhance the improved bilinear neural network method by using a large number of activation functions instead of neurons. This method incorporates the concept of simulating more complicated activation functions with fewer parameters, with more diverse activation functions to generate more complex and rare analytical solutions. On this basis, constraints are introduced into the method, reducing a significant amount of computational workload. We also construct neural network architectures, such as “2–3–1,” “2–2–3–1,” “2–3–3–1,” and “2–3–2–1” using this method. Maple software is employed to obtain many exact analytical solutions by selecting appropriate parameters, such as the superposition of double-period lump solutions, lump–rogue wave solutions, and three interaction solutions. The results show that these solutions exhibit more complex waveforms than those obtained by conventional methods, which is of great significance for the electrical systems and multicomponent fluids to which the equation is applied. This novel method shows significant advantages when applied to fractional-order equations and is expected to be increasingly widely used in the study of nonlinear partial differential equations.

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New type of rogue waves

Cited by 4 publications

References 45 publications

Dynamical analysis of solitons, breathers and periodic rogue waves for the variable-coefficient fourth-order nonlinear Schrödinger equation

Dynamical analysis of solitons, breathers and periodic rogue waves for the variable-coefficient fourth-order nonlinear Schrödinger equation

Double-pole dark-bright mixed solitons for a three-wave-resonant-interaction system

Interactions of localized wave and dynamics analysis in the new generalized stochastic fractional potential-KdV equation

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