Rogue Waves in the Generalized Derivative Nonlinear Schrödinger Equations
نویسندگان
چکیده
منابع مشابه
Rogue waves for a system of coupled derivative nonlinear Schrödinger equations.
Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schrödinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics, plasmas, etc., exhibits RWs only in the regime of modulation instability (MI) of the background. For a system of multiple waveguides, the governing coupled NLSEs can produce regimes ...
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We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear Schrödinger equation and present explicit forms for these solutions from first to fourth order. We also explain their relation to the highest amplitude part of a field that starts with a plane wave perturbed by random small amplitude radiation waves. Our work can elucidate the appearance of rogue ...
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Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrödinger equation with positive linear dispersion in the regime of positive cubic nonlinearity. Rogue waves of a derivative nonlinear Schrödinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur ...
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Weak interactions of solitary waves in the generalized nonlinear Schrödinger equations are studied. It is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities. Then by using the Karpman-Solov'ev method, a universal system of dynamical equations is derived for the velocities, amplitudes, positions, and phases of interacting sol...
متن کاملRogue waves for a system of coupled derivative nonlinear Schrӧdinger equations
Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schrödinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics and plasmas, exhibits RWs only in the regime of modulation instability (MI) of the background. For system of multiple waveguides, the governing coupled NLSEs can produce regimes of MI...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Science
سال: 2020
ISSN: 0938-8974,1432-1467
DOI: 10.1007/s00332-020-09643-8