Integrable variable-coefficient coupled cylindrical NLS equations and their explicit solutions

2014 ◽  
Vol 30 (4) ◽  
pp. 1017-1024 ◽  
Author(s):  
Ting Su ◽  
Guo-hua Ding ◽  
Jian-yin Fang
Keyword(s):  
Variable Coefficient ◽  
Explicit Solutions

scholarly journals ON THE APPLICATION OF A GENERALIZED VERSION OF THE DRESSING METHOD TO THE INTEGRATION OF VARIABLE COEFFICIENT N-COUPLED NONLINEAR SCHRÖDINGER EQUATION

2012 ◽  
Vol 19 (04) ◽  
pp. 1250028
Author(s):  
TING SU ◽  
HUIHUI DAI ◽  
XIAN GUO GENG
Keyword(s):  
Optical Fibers ◽  
Variable Coefficient ◽  
High Order ◽  
Explicit Solutions ◽  
Compatibility Conditions ◽  
Dressing Method ◽  
Integrable Equations ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Hirota Equations

N-coupled nonlinear Schrödinger (NLS) equations have been proposed to describe N-pulse simultaneous propagation in optical fibers. When the fiber is nonuniform, N-coupled variable-coefficient NLS equations can arise. In this paper, a family of N-coupled integrable variable-coefficient NLS equations are studied by using a generalized version of the dressing method. We first extend the dressing method to the versions with (N + 1) × (N + 1) operators and (2N + 1) × (2N + 1) operators. Then, we obtain three types of N-coupled variable-coefficient equations (N-coupled NLS equations, N-coupled Hirota equations and N-coupled high-order NLS equations). Then, the compatibility conditions are given, which insure that these equations are integrable. Finally, the explicit solutions of the new integrable equations are obtained.

Integrable variable-coefficient derivative Spin-1 Gross–Pitaevskii equations and their explicit solutions

2021 ◽  
Author(s):  
Ting Su ◽  
Junhong Yao ◽  
Yanan Huang
Keyword(s):  
Variable Coefficient ◽  
Separation Of Variables ◽  
Lax Pair ◽  
Explicit Solutions ◽  
Dressing Method

Based on the generalized dressing method, we propose a new integrable variable coefficient Spin-1 Gross–Pitaevskii equations and derive their Lax pair. Using separation of variables, we have derived explicit solutions of the equations. In order to analyze the characteristic of derived solution, the graphical wave of the solutions is plotted with the aid of Matlab.

Truncated Painlevé Expansion with Symbolic Computation for a General Kadomtsev-Petviashvili Equation with Variable Coefficients

1996 ◽  
Vol 51 (3) ◽  
pp. 175-178
Author(s):  
Bo Tian ◽  
Yi-Tian Gao
Keyword(s):  
Symbolic Computation ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Variable Coefficients ◽  
Explicit Solutions ◽  
Current Interest ◽  
Backlund Transformation ◽  
Petviashvili Equation ◽  
Mathematical Sciences ◽  
Truncated Painlevé Expansion

Able to realistically model various physical situations, the variable-coefficient generalizations of the celebrated Kadmotsev-Petviashvili equation are of current interest in physical and mathematical sciences. In this paper, we make use of both the truncated Painleve expansion and symbolic computation to obtain an auto-Bäcklund transformation and certain soliton-typed explicit solutions for a general Kadomtsev-Petviashvili equation with variable coefficients.

Explicit Analytical Solutions of Linear and Nonlinear Interior Heat and Mass Transfer Equation Sets for Drying Process

2003 ◽  
Vol 125 (1) ◽  
pp. 175-178 ◽  
Author(s):  
Ruixian Cai ◽  
Na Zhang
Keyword(s):  
Analytical Solutions ◽  
Variable Coefficient ◽  
Infinite Plate ◽  
Explicit Solutions ◽  
Drying Process ◽  
Mass Transfer Equation ◽  
Mathematical Skills ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
Dimensional Variable

Some algebraic explicit analytical solutions of the unsteady one-dimensional variable coefficient partial differential equation set describing drying process of an infinite plate are derived and given. Such explicit solutions have not yet been published before. Besides their irreplaceable theoretical value, analytical solutions can also serve as benchmark to check the results of recently rapidly developing numerical calculation and study various computational methods. In addition, some mathematical skills used in this paper are special and deserve further attention.

scholarly journals A New Integrable Variable-Coefficient 2+1-Dimensional Long Wave-Short Wave Equation and the Generalized Dressing Method

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ting Su ◽  
Hui Hui Dai
Keyword(s):  
Wave Equation ◽  
Variable Coefficient ◽  
Separation Of Variables ◽  
Short Wave ◽  
Lax Pair ◽  
Explicit Solutions ◽  
Dressing Method ◽  
Long Wave

Based on the generalized dressing method, we propose a new integrable variable-coefficient 2+1-dimensional long wave-short wave equation and derive its Lax pair. Using separation of variables, we have derived the explicit solutions of the equation. With the aid of Matlab, the curves of the solutions are drawn.

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