Optical solitons, complexitons and power series solutions of a (2+1)-dimensional nonlinear Schrödinger equation

2018 ◽  
Vol 32 (28) ◽  
pp. 1850336 ◽  
Author(s):  
Wei-Qi Peng ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dynamical Behavior ◽  
Nonlinear Schrodinger Equation ◽  
Series Solutions ◽  
Ansatz Method ◽  
Nonlinear Schrödinger ◽  
Power Series Solutions

In this paper, a (2+1)-dimensional generalized nonlinear Schrödinger equation is investigated, which is an important model in the field of optical fiber propagation. By employing the ansatz method, we obtain the bright soliton, dark soliton and complexiton of the equation. Some constraint conditions are also derived to ensure the existence of the solitons. Moreover, its power series solutions with the convergence analysis are also provided. Some graphical analyses of those solutions are presented in order to better understand their dynamical behavior.

Optical solitons, complexitons and power series solutions of the perturbed nonlinear Schrödinger equation

2018 ◽  
Vol 32 (21) ◽  
pp. 1850243
Author(s):  
Hui Wang ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Power Series Solution ◽  
Ansatz Method ◽  
Nonlinear Schrödinger

In this paper, we consider the perturbed nonlinear Schrödinger equation with a bounded potential, which is an important model in fiber communication. By considering the ansatz method, we obtain the bright and dark soliton solutions of the equation. By employing the sub-equation method, we also construct its complexitons solutions. Finally, the explicit power series solution is also derived with its convergence analysis. It is hoped that our results can help enrich the nonlinear dynamical behaviors of the perturbed nonlinear Schrödinger equation.

DARK AND BRIGHT SOLITARY WAVE SOLUTIONS OF THE HIGHER ORDER NONLINEAR SCHRÖDINGER EQUATION WITH SELF-STEEPENING AND SELF-FREQUENCY SHIFT EFFECTS

2013 ◽  
Vol 22 (01) ◽  
pp. 1350001 ◽  
Author(s):  
HITENDER KUMAR ◽  
FAKIR CHAND
Keyword(s):  
Solitary Wave ◽  
Schrödinger Equation ◽  
Frequency Shift ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Ansatz Method ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

In this paper, we obtain the exact bright and dark soliton solutions for the nonlinear Schrödinger equation (NLSE) which describes the propagation of femtosecond light pulses in optical fibers in the presence of self-steepening and a self-frequency shift terms. The solitary wave ansatz method is used to carry out the derivations of the solitons. The parametric conditions for the formation of soliton pulses are determined. Using the one-soliton solution, a number of conserved quantities have been calculated for Hirota and Sasa–Satsuma cases and finally, we have constructed some periodic wave solutions by reducing the higher order nonlinear Schrödinger equation (HNLS) to quartic anharmonic oscillator equation. The obtained exact solutions may be useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in a HNLS model equation.

scholarly journals Multiple Accurate-Cubic Optical Solitons to the Kerr-Low and Power-low Nonlinear Schrodinger Equation without the Chromatic Dispersion

2021 ◽  
Author(s):  
Emad H.M. Zahran ◽  
Ahmet Bekir
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Power Law ◽  
Schrodinger Equation ◽  
Chromatic Dispersion ◽  
Optical Solitons ◽  
Nonlinear Schrodinger Equation ◽  
Ansatz Method ◽  
Nonlinear Schrödinger ◽  
Kerr Law

Abstract The main target of this work is implementing multiple accurate cubic optical solitons for the nonlinear Schrödinger equation in the presence of third-order dispersion effects, absence of the chromatic dispersion. The emergence cubic optical solitons of the proposed model are extracted for the kerr-law and power law nonlinearity in the framework of two distinct techniques, the first one is the extended simple equation method (ESEM), while the other is the solitary wave ansatz method (SWAM). These cubic optical solitons for the kerr-law and power law nonlinearity have been extracted successfully at the same time and parallel via these two different techniques. A good comparison not only between our achieved results by these two manners but also with that achieved previously has been extracted. .

PARAMETRICALLY DRIVEN INSTABILITY IN QUASI-REVERSAL SYSTEMS

2009 ◽  
Vol 19 (10) ◽  
pp. 3525-3532 ◽  
Author(s):  
MARCEL G. CLERC ◽  
SALIYA COULIBALY ◽  
DAVID LAROZE
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dynamical Behavior ◽  
Parametric Instability ◽  
Amplitude Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Driven System ◽  
Good Agreement

Parametric instability of quasi-reversal system — i.e. time reversible systems perturbed with injection and dissipation of energy — is studied in a unified manner. We infer and characterize an adequate amplitude equation, which is the parametrically driven damped nonlinear Schrödinger equation, corrected with higher order terms. This model exhibits rich dynamical behavior which are lost in the parametrically driven damped nonlinear Schrödinger equation such as: uniform states, fronts and coherent states. The dynamical behavior of a simple parametrically driven system, the vertically driven chain of pendula, exhibits quite good agreement with the amended amplitude equation.

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