scholarly journals Explicit Wave Solutions and Qualitative Analysis of the (1 + 2)-Dimensional Nonlinear Schrödinger Equation with Dual-Power Law Nonlinearity

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Qing Meng ◽  
Bin He ◽  
Zhenyang Li
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Power Law ◽  
Bifurcation Theory ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Point Of View ◽  
Phase Portraits ◽  
Nonlinear Schrödinger ◽  
Dual Power

The (1 + 2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity is studied using the factorization technique, bifurcation theory of dynamical system, and phase portraits analysis. From a dynamic point of view, the existence of smooth solitary wave, and kink and antikink waves is proved and all possible explicit parametric representations of these waves are presented.

Study of modulation instability analysis and optical soliton solutions of higher-order dispersive nonlinear Schrödinger equation with dual-power law nonlinearity

2019 ◽  
Vol 33 (25) ◽  
pp. 1950309
Author(s):  
Naila Nasreen ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Power Law ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Mapping Technique ◽  
Nonlinear Schrödinger ◽  
Dual Power

In this paper, based on proposed Riccati mapping technique, we investigated the soliton solutions of fourth-order dispersive nonlinear Schrödinger equation with nonlinearity of dual-power law. The various types of solitons solutions involving some parameters are constructed. These soliton solutions can be useful for understanding the physical nature of the waves spread in the dispersive medium. Furthermore, the Modulation Instability (MI) is discussed by standard linear-stability analysis that shows all achieved results are exact and stable. The movements of some achieved results were presented graphically by giving suitable values to parameters that provide easy understanding to the physical phenomenon of this dynamical model. The obtained results show the simplicity and efficiency of the current used approach.

A novel method for new solutions of time fractional (1+2)-dimensional nonlinear Schrödinger equation involving dual-power law nonlinearity

2019 ◽  
Vol 33 (24) ◽  
pp. 1950280
Author(s):  
S. Saha Ray
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Power Law ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Jacobi Elliptic Function ◽  
Nonlinear Schrödinger ◽  
Novel Method ◽  
Dual Power

In this paper, a novel method has been used to solve time fractional [Formula: see text]-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity. Using the newly-proposed Jacobi elliptic function expansion method, new double periodic, bright and soliton solutions of the aforesaid equation have been obtained. The results show that the proposed method is a convenient, efficient and straightforward technique to devise new soliton solutions of the presently-mentioned equation.

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