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Characteristics of the breather and rogue waves in a \((2+1)\)-dimensional nonlinear Schrödinger equation. (English) Zbl 1392.35296
Summary: Under investigation in this paper is a \((2+1)\)-dimensional nonlinear Schrödinger equation (NLS), which is a generalisation of the NLS equation. By virtue of Wronskian determinants, an effective method is presented to succinctly construct the breather wave and rogue wave solutions of the equation. Furthermore, the main characteristics of the breather and rogue waves are graphically discussed. The results show that rogue waves can come from the extreme behavior of the breather waves. It is hoped that our results could be useful for enriching and explaining some related nonlinear phenomena.

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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