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- W4386701495 abstract "Effects of nonlinear dynamics of solitary waves and wave modulations within the modular (also known as quadratically cubic) Korteweg-de Vries equation are studied analytically and numerically. Large wave events can occur in the course of interaction between solitons of different signs. Stable and unstable (finite-time-lived) breathers can be generated in inelastic collisions of solitons and from perturbations of two polarities. A nonlinear evolution equation on long modulations of quasi-sinusoidal waves is derived, which is the modular or quadratically cubic nonlinear Schrödinger equation. Its solutions in the form of envelope solitons describe breathers of the modular Korteweg-de Vries equation. The instability conditions are obtained from the linear stability analysis of periodic wave perturbations. Rogue-wave-type solutions emerging due to the modulational instability in the modular Korteweg-de Vries equation are simulated numerically. They exhibit similar wave amplification, but develop faster than in the Benjamin – Feir instability described by the cubic nonlinear Schrödinger equation." @default.
- W4386701495 created "2023-09-14" @default.
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- W4386701495 date "2023-12-01" @default.
- W4386701495 modified "2023-10-16" @default.
- W4386701495 title "Nonlinear waves, modulations and rogue waves in the modular Korteweg-de Vries equation" @default.
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- W4386701495 doi "https://doi.org/10.1016/j.cnsns.2023.107527" @default.
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