scholarly journals Rogue waves and rational solutions of the nonlinear Schrödinger equation

2009 ◽  
Vol 80 (2) ◽  
Author(s):  
Nail Akhmediev ◽  
Adrian Ankiewicz ◽  
J. M. Soto-Crespo
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Nonlinear Schrödinger

Breathers, rogue waves and their dynamics in a (2+1)-dimensional nonlinear Schrödinger equation

2020 ◽  
Vol 34 (23) ◽  
pp. 2050234
Author(s):  
Yong Chen ◽  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Plane Wave Solution ◽  
Nonlinear Schrödinger ◽  
Wave Phenomena

Under investigation in this paper is a (2[Formula: see text]+[Formula: see text]1)-dimensional nonlinear Schrödinger equation, which is a generalization of the standard nonlinear Schrödinger equation. By means of the modified Darboux transformation, the hierarchies of rational solutions and breather solutions are generated from the plane wave solution. Furthermore, the main characteristics of the nonlinear waves including the Akhmediev breathers, Kuznetsov–Ma solitons, and their combined structures are graphically discussed. Our results would be of much importance in enriching and explaining rogue wave phenomena in nonlinear wave fields.

Rational Solutions and Rogue Waves in Nonlinear Schrödinger Equation With Varying Coefficients

2014 ◽  
Author(s):  
Ni Song ◽  
Wei Zhang ◽  
Sha. Zhou ◽  
Qian Wang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Formation Mechanisms ◽  
Rational Solutions ◽  
Nonlinear Schrödinger ◽  
Varying Coefficients

The similarity transformation and direct ansatz are applied to obtain rogue wave solutions of nonlinear Schrödinger equation with varying coefficients. These obtained solutions can be used to describe the possible formation mechanisms for optical rogue wave phenomenon in optical fibres. Moreover their dynamical behaviors are exhibited for chosen different functions. This will further excite the possibility of relative researchers and potential applications of rogue waves in other related fields.

Rational soliton solutions of the nonlocal nonlinear Schrödinger equation by the KP reduction method

2019 ◽  
Vol 33 (30) ◽  
pp. 1950362
Author(s):  
Donghua Wang ◽  
Yehui Huang ◽  
Xuelin Yong ◽  
Jinping Zhang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Reduction Method ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

In this paper, we present the construction of the rational solutions to the nonlocal nonlinear Schrödinger equation by the bilinear method and KP reduction method. The solutions are given in determinant form, the first- and second-order rational solutions are analyzed for their dynamic behaviors.

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