Extreme waves statistics for the Ablowitz-Ladik system
نویسندگان
چکیده
منابع مشابه
Discrete rogue waves of the Ablowitz-Ladik and Hirota equations.
We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which inc...
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An efficient formalism is elaborated to analytically describe dynamics of the Ablowitz-Ladik soliton in the presence of perturbations. This formalism is based on using the Riemann-Hilbert problem and provides the means of calculating evolution of the discrete soliton parameters, as well as shape distortion and perturbation-induced radiation effects. As an example, soliton characteristics are ca...
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Abstract. We study the Poisson structure associated to the defocusing Ablowitz-Ladik equation from a functional-analytical point of view, by reexpressing the Poisson bracket in terms of the associated Carathéodory function. Using this expression, we are able to introduce a family of compatible Poisson brackets which form a multi-Hamiltonian structure for the Ablowitz-Ladik equation. Furthermore...
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The question of constructing the finite genus quasiperiodic solutions for the Ablo-witz-Ladik hierarchy (ALH) is considered by establishing relations between the ALH and the Fay's identity for the θ-functions. It is shown that using a limiting procedure one can derive from the latter an infinite number of differential identities which can be arranged as an infinite set of differential-differenc...
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A model of two coupled Ablowitz-Ladik (AL) lattices is introduced. While the system as a whole is not integrable, it admits reduction to the integrable AL model for symmetric states. Stability and evolution of symmetric solitons are studied in detail analytically (by means of a variational approximation) and numerically. It is found that there exists a finite interval of positive values of the ...
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ژورنال
عنوان ژورنال: JETP Letters
سال: 2014
ISSN: 0021-3640,1090-6487
DOI: 10.1134/s0021364013240028