Soliton trapping, transmission and wake in modulationally unstable media

Abstract

Interactions between solitons and the coherent oscillation structures generated by localized disturbances via modulational instability are studied within the framework of the focusing nonlinear Schrodinger equation. Two main interaction regimes are identified based on the relative value of the velocity of the incident soliton compared to the amplitude of the background: soliton transmission and soliton trapping. Specifically, when the incident soliton velocity exceeds a certain threshold, the soliton passes through the coherent structure and emerges on the other side with its velocity unchanged. Conversely, when the incident soliton velocity is below the threshold, once the soliton enters the coherent structure, it remains confined there forever. It is demonstrated that the soliton is not destroyed, but its velocity inside the coherent structure is different from its initial one. Moreover, it is also shown that, depending on the location of the discrete eigenvalue associated to the soliton, these phenomena can also be accompanied by the generation of additional, localized propagating waves in the coherent structure, akin to a soliton-generated wake.

arXiv comment8 pages, 8 figures, to appear in Phys. Rev. E

References in corpus (9)

• Dispersive shock waves and modulation theory
• On the nonlinear stage of Modulation Instability
• Integrable turbulence and formation of rogue waves
• Universal nature of the nonlinear stage of modulational instability
• Solitonic dispersive hydrodynamics: theory and observation
• Formation of rogue waves from the locally perturbed condensate
• Hydrodynamic Optical Soliton Tunneling
• A numerical dressing method for the nonlinear superposition of solutions of the KdV equation
• Solitons, the Korteweg-de Vries equation with step boundary values and pseudo-embedded eigenvalues

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