Abundant explicit exact solutions to the generalized nonlinear Schrödinger equation with parabolic law and dual-power law nonlinearities

2014 ◽  
Vol 38 (2) ◽  
pp. 296-310 ◽  
Author(s):  
Xiaoxiao Zheng ◽  
Yadong Shang
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Power Law ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Parabolic Law ◽  
Generalized Nonlinear Schrödinger Equation ◽  
Dual Power

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.

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