scholarly journals Exact Solutions of the Generalized Nonlinear Schrodinger Equation

2021 ◽  
pp. 18-25
Author(s):  
Gaukhar Shaikhova ◽  
Arailym Syzdykova ◽  
Samgar Daulet
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Physical Problems ◽  
Different Types ◽  
Generalized Nonlinear Schrödinger Equation

In this work, the generalized nonlinear Schrodinger equation is investigated. Exact solutions are derived by the sinecosine method. This method is used to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The obtained solutions are found to be important for the explanation of some practical physical problems.

BIFURCATION, EXACT SOLUTIONS AND NONSMOOTH BEHAVIOR OF SOLITARY WAVES IN THE GENERALIZED NONLINEAR SCHRÖDINGER EQUATION

2005 ◽  
Vol 15 (10) ◽  
pp. 3295-3305 ◽  
Author(s):  
WEI WANG ◽  
JIANHUA SUN ◽  
GUANRONG CHEN
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Solitary Waves ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Heteroclinic Orbits ◽  
Nonlinear Schrödinger ◽  
Generalized Nonlinear Schrödinger Equation ◽  
Planar Dynamical Systems

In this paper, the generalized nonlinear Schrödinger equation (GNLS) is studied. The bifurcation of solitary waves of the equation is discussed first, by using the bifurcation theory of planar dynamical systems. Then, the respective numbers of solitary waves are derived under different conditions on the equation parameters. Exact solutions of smooth solitary waves are obtained in the explicit form of a(ξ)ei(ψ(ξ)-ωt), ξ = x - vt by qualitatively seeking the homoclinic and heteroclinic orbits for a class of Liénard equations. Finally, nonsmooth solitary wave solutions of the GNLS are investigated.

scholarly journals Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

2018 ◽  
Vol 48 (1) ◽  
pp. 59-68 ◽  
Author(s):  
Nikolay K. Vitanov ◽  
Zlatinka I. Dimitrova
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Deep Water ◽  
Water Waves ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Modified Method

AbstractWe consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

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