scholarly journals Discrete Spectrum of 2 + 1-Dimensional Nonlinear Schrödinger Equation and Dynamics of Lumps

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Javier Villarroel ◽  
Julia Prada ◽  
Pilar G. Estévez
Keyword(s):  
Schrödinger Equation ◽  
Discrete Spectrum ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Body Problem ◽  
Dynamical Evolution ◽  
Nonlinear Schrodinger Equation ◽  
Spectral Operator ◽  
Nonlinear Schrödinger ◽  
Integrable Generalization

We consider a natural integrable generalization of nonlinear Schrödinger equation to2+1dimensions. By studying the associated spectral operator we discover a rich discrete spectrum associated with regular rationally decaying solutions, the lumps, which display interesting nontrivial dynamics and scattering. Particular interest is placed in the dynamical evolution of the associated pulses. For all cases under study we find that the relevant dynamics corresponds to acentral configurationof a certainN-body problem.

New types of chirped soliton solutions for the Fokas–Lenells equation

2017 ◽  
Vol 27 (7) ◽  
pp. 1596-1601 ◽  
Author(s):  
Houria Triki ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Efficient Algorithm ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Content Type ◽  
Nonlinear Schrödinger ◽  
Integrable Generalization ◽  
Temporal Dispersion

Purpose The purpose of this paper is to present a reliable treatment of the Fokas–Lenells equation, an integrable generalization of the nonlinear Schrödinger equation. The authors use a special complex envelope traveling-wave solution to carry out the analysis. The study confirms the accuracy and efficiency of the used method. Design/methodology/approach The proposed technique, namely, the trial equation method, as presented in this work has been shown to be very efficient for solving nonlinear equations with spatio-temporal dispersion. Findings A class of chirped soliton-like solutions including bright, dark and kink solitons is derived. The associated chirp, including linear and nonlinear contributions, is also determined for each of these optical pulses. Parametric conditions for the existence of chirped soliton solutions are presented. Research limitations/implications The paper presents a new efficient algorithm for handling an integrable generalization of the nonlinear Schrödinger equation. Practical/implications The authors present a useful algorithm to handle nonlinear equations with spatial-temporal dispersion. The method is an effective method with promising results. Social/implications This is a newly examined model. A useful method is presented to offer a reliable treatment. Originality/value The paper presents a new efficient algorithm for handling an integrable generalization of the nonlinear Schrödinger equation.

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