Rogue waves in the Davey-Stewartson I equation

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Rogue 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...

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Dynamics of rogue waves in the Davey–Stewartson II equation

General rogue waves in the Davey–Stewartson (DS)II equation are derived by the bilinear method, and the solutions are given through determinants. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background in a line profile and then retreat back to the constant background again. It is also shown that multi-rogue waves describe the intera...

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The Fourier Method for the Linearized Davey-stewartson I Equation

The linearized Davey-Stewartson equation with varing coefficients is solved by Fourier method. The approach uses the inverse scattering transform for the Davey-Stewartson equation.

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Finite-dimensional integrable systems associated with Davey-Stewartson I equation

For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1 dimensional system to get three 1+0 dimensional Hamiltonian systems with a constraint of Neumann type. The full set of involutive conserved integrals is obtained ...

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Davey-Stewartson Equation with Fractional Coordinate Derivatives

We have used the homotopy analysis method (HAM) to obtain solution of Davey-Stewartson equations of fractional order. The fractional derivative is described in the Caputo sense. The results obtained by this method have been compared with the exact solutions. Stability and convergence of the proposed approach is investigated. The effects of fractional derivatives for the systems under considerat...

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ژورنال

عنوان ژورنال: Physical Review E

سال: 2012

ISSN: 1539-3755,1550-2376

DOI: 10.1103/physreve.86.036604