scholarly journals Solitons of the resonant nonlinear Schrödinger equation with nontrivial boundary conditions: Hirota bilinear method

2007 ◽  
Vol 152 (1) ◽  
pp. 991-1003 ◽  
Author(s):  
J.-H. Lee ◽  
O. K. Pashaev
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Hirota Bilinear Method ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Hirota Bilinear

EXACT DARK SOLITON SOLUTION OF THE GENERALIZED NONLINEAR SCHRÖDINGER EQUATION

2009 ◽  
Vol 23 (24) ◽  
pp. 2869-2888 ◽  
Author(s):  
YI ZHANG ◽  
XIAO-NA CAI ◽  
CAI-ZHEN YAO ◽  
HONG-XIAN XU
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Dark Soliton ◽  
Nonlinear Schrodinger Equation ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Generalized Nonlinear Schrödinger Equation ◽  
Hirota Bilinear

The generalized nonlinear Schrödinger equation with the variable coefficient is discussed, and the exact dark N-soliton solution is presented by using the Hirota bilinear method, from finding the 1-soliton to 2-soliton, and then we obtain the N-soliton solution. With the aid of Maple, a few figures of solutions under several different cases are shown when aleatoric constants and variables are given exact values.

EXPECTED AND UNEXPECTED SOLUTIONS TO THE STATIONARY ONE-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1663-1667
Author(s):  
LINCOLN D. CARR ◽  
CHARLES W. CLARK ◽  
WILLIAM P. REINHARDT
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stationary Solutions ◽  
Einstein Condensate ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Bose Einstein Condensate ◽  
Dilute Gas

We present all stationary solutions to the nonlinear Schrödinger equation in one dimension for box and periodic boundary conditions. For both repulsive and attractive nonlinearity we find expected and unexpected solutions. Expected solutions are those that are in direct analogy with those of the linear Schödinger equation under the same boundary conditions. Unexpected solutions are those that have no such analogy. We give a physical interpretation for the unexpected solutions. We discuss the properties of all solution types and briefly relate them to experiments on the dilute-gas Bose-Einstein condensate.

Rational soliton solutions of the nonlocal nonlinear Schrödinger equation by the KP reduction method

2019 ◽  
Vol 33 (30) ◽  
pp. 1950362
Author(s):  
Donghua Wang ◽  
Yehui Huang ◽  
Xuelin Yong ◽  
Jinping Zhang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Reduction Method ◽  
Nonlinear Schrodinger Equation ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

In this paper, we present the construction of the rational solutions to the nonlocal nonlinear Schrödinger equation by the bilinear method and KP reduction method. The solutions are given in determinant form, the first- and second-order rational solutions are analyzed for their dynamic behaviors.

scholarly journals The soliton solution of a modified nonlinear schrödinger equation

2017 ◽  
Vol 5 (1) ◽  
pp. 16
Author(s):  
Jumei Zhang ◽  
Li Yin
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Equations ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Derivative Method ◽  
Hirota Bilinear

Hirota bilinear derivative method can be used to construct the soliton solutions for nonlinear equations. In this paper we construct the soliton solutions of a modified nonlinear Schrödinger equation by bilinear derivative method.

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