Analytical study of the nonlinear Schrödinger equation with an arbitrary linear time-dependent potential in quasi-one-dimensional Bose–Einstein condensates

2008 ◽  
Vol 323 (10) ◽  
pp. 2554-2565 ◽  
Author(s):  
Xing Lü ◽  
Bo Tian ◽  
Tao Xu ◽  
Ke-Jie Cai ◽  
Wen-Jun Liu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Analytical Study ◽  
Linear Time ◽  
Nonlinear Schrodinger Equation ◽  
Time Dependent ◽  
One Dimensional ◽  
Dependent Potential ◽  
Bose Einstein

scholarly journals Rogue Waves of Nonlinear Schrödinger Equation with Time-Dependent Linear Potential Function

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Ni Song ◽  
Yakui Xue
Keyword(s):  
Schrödinger Equation ◽  
Potential Function ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Time Dependent ◽  
Linear Potential ◽  
Nonlinear Schrödinger ◽  
Bose Einstein

The rogue waves of the nonlinear Schrödinger equation with time-dependent linear potential function are investigated by using the similarity transformation in this paper. The first-order and second-order rogue waves solutions are obtained and the nonlinear dynamic behaviors of these solutions are discussed in detail. In addition, the amplitudes of the rogue waves under the effect of the gravity field and external magnetic field changing with the time are analyzed by using numerical simulation. The results can be used to study the matter rogue waves in the Bose-Einstein condensates and other fields of nonlinear science.

scholarly journals On the Existence of Bright Solitons in Cubic-Quintic Nonlinear Schrödinger Equation with Inhomogeneous Nonlinearity

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Juan Belmonte-Beitia
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Bifurcation Theory ◽  
Schrodinger Equation ◽  
Chemical Potential ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Bose Einstein ◽  
Quintic Nonlinear Schrödinger Equation

We give a proof of the existence of stationary bright soliton solutions of the cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity. By using bifurcation theory, we prove that the norm of the positive solution goes to zero as the parameterλ, called chemical potential in the Bose-Einstein condensates' literature, tends to zero. Moreover, we solve the time-dependent cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearities by using a numerical method.

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