Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation
نویسندگان
چکیده
منابع مشابه
Rogue waves and rational solutions of the Hirota equation.
The Hirota equation is a modified nonlinear Schrödinger equation (NLSE) that takes into account higher-order dispersion and time-delay corrections to the cubic nonlinearity. In describing wave propagation in the ocean and optical fibers, it can be viewed as an approximation which is more accurate than the NLSE. We have modified the Darboux transformation technique to show how to construct the h...
متن کاملRogue waves and rational solutions of the nonlinear Schrödinger equation.
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 ...
متن کاملRogue waves in the Davey-Stewartson I equation.
General rogue waves in the Davey-Stewartson-I equation are derived by the bilinear method. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background with a line profile and then disappear into the constant background again. It is also shown that multirogue waves describe the interaction of several fundamental rogue waves. These multiro...
متن کاملRogue periodic waves of the mKdV equation
Rogue periodic waves stand for rogue waves on the periodic background. Two families of traveling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and twofold Darboux transformations, we construct explicitly the rogue periodic waves of the mKdV equation. Since the dn-periodic wave i...
متن کاملOn Finite Energy Solutions of the Kp - I Equation
We prove that the flow map of the Kadomtsev-Petviashvili-I (KP-I) equation is not uniformly continuous on bounded sets of the natural energy space.
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ژورنال
عنوان ژورنال: Natural Hazards and Earth System Sciences
سال: 2011
ISSN: 1684-9981
DOI: 10.5194/nhess-11-667-2011