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Theoretical modeling reveals localized breather and rogue wave solutions in the Kundu-nonlinear Schrödinger equation, indicating broad applications across optics and fluid dynamics.
Under investigation in this work is the Kundu-nonlinear Schrödinger equation, which can be reduced to the standard nonlinear Schrödinger equation. Through the Darboux-dressing transformation, we obtain and discuss the localized wave solutions of the equation. This family of solutions can include known Peregrine soliton (i.e., Rogue waves), Akhmediev breather, Kuznetsov–Ma soliton. Moreover, the main characteristics of these rational solutions are discussed with some graphics. These solutions should be of great interest in a variety of complex systems, from optics and fluid dynamics to Bose–Einstein condensates and finance.
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Wang et al. (2019) studied this question.
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