Dark soliton solution of Sasa-Satsuma equation

2010 ◽  
Author(s):  
Y. Ohta ◽  
Wen Xiu Ma ◽  
Xing-biao Hu ◽  
Qingping Liu
Keyword(s):  
Soliton Solution ◽  
Dark Soliton

BIFURCATIONS OF TRAVELING WAVE SOLUTIONS AND EXACT SOLUTIONS FOR THE GENERALIZED SCHRÖDINGER EQUATION

2011 ◽  
Vol 21 (09) ◽  
pp. 2623-2628
Author(s):  
JIANMING ZHANG ◽  
SHUMING LI
Keyword(s):  
Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Traveling Wave Solutions ◽  
Dark Soliton ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Generalized Schrödinger Equation ◽  
Bright Soliton Solution

Using the method of dynamical systems for the generalized Schrödinger equation, the bright soliton solution, dark soliton solution, uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. Exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

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.

scholarly journals Some analytical solutions by mapping methods for non-linear conformable time-fractional PHI-4 equation

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1815-1822 ◽  
Author(s):  
Zeliha Korpinar
Keyword(s):  
Fractional Derivative ◽  
Periodic Solutions ◽  
Soliton Solution ◽  
Analytical Solutions ◽  
Soliton Solutions ◽  
Elliptic Functions ◽  
Dark Soliton ◽  
Optical Soliton ◽  
Conformable Fractional Derivative ◽  
Singular Soliton

In this paper, the practice of two types of mapping methods are used to solve the time fractional Phi-4 equation by means of conformable fractional derivative. The solutions are derived using Jacobi?s elliptic functions for two different value of the modulus and are obtained the some soliton solutions. The found solutions are iden?tified bright optical soliton, dark soliton, singular soliton, combo soliton solution, and periodic solutions.

Dark soliton dynamics for quantum systems with higher-order dispersion and higher-order nonlinearity

2021 ◽  
pp. 2150284
Author(s):  
Chen Chen ◽  
Guojun Gao ◽  
Ying Wang ◽  
Yuqi Pan ◽  
Shuyu Zhou
Keyword(s):  
Soliton Solution ◽  
Dark Soliton ◽  
Quantum Systems ◽  
Higher Order ◽  
High Order ◽  
Nonlinear Interactions ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One ◽  
Order Dispersion

In this work, we investigated one-dimensional and two-dimensional quantum systems with higher-order dispersions and higher-order nonlinear interactions. Based on the high-order nonlinear Schrödinger equation (NLSE) and via the [Formula: see text]-expansion method, we derived the analytical dark soliton solution for the one-dimensional system first. By applying the self-similar method and using the results of the one-dimensional case, the analytical dark soliton solution of the system in the two-dimensional case was derived. The dynamic evolution pattern of the two-dimensional dark soliton is pictorially demonstrated. The theoretical results of our work can be used to guide the detection and experimental study of dark soliton in a two-dimensional quantum system, using high-order dispersion and higher-order nonlinear interactions.

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