Multi-soliton solutions and a Bäcklund transformation for a generalized variable-coefficient higher-order nonlinear Schrödinger equation with symbolic computation

2008 ◽  
Vol 387 (1) ◽  
pp. 97-107 ◽  
Author(s):  
Xiang-Hua Meng ◽  
Wen-Jun Liu ◽  
Hong-Wu Zhu ◽  
Chun-Yi Zhang ◽  
Bo Tian
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Symbolic Computation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Bäcklund Transformation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Backlund Transformation

ANALYTIC DARK SOLITON SOLUTIONS FOR A GENERALIZED VARIABLE-COEFFICIENT HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION IN OPTICAL FIBERS USING SYMBOLIC COMPUTATION

2011 ◽  
Vol 25 (04) ◽  
pp. 499-509 ◽  
Author(s):  
XIANG-HUA MENG ◽  
ZHI-YUAN SUN ◽  
CHUN-YI ZHANG ◽  
BO TIAN
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Symbolic Computation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Bilinear Method ◽  
Nonlinear Schrödinger

In this paper, a generalized variable-coefficient nonlinear Schrödinger equation with higher-order and gain/loss effects which can be used to describe the femtosecond pulse propagation is analytically investigated via symbolic computation. Under sets of coefficient constraints, such an equation is transformed into a completely integrable constant-coefficient higher-order nonlinear Schrödinger equation. Furthermore, through the transformation, the dark one- and two-soliton solutions for the generalized variable-coefficient higher-order nonlinear Schrödinger equation are derived by means of the bilinear method.

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