Darboux transformation and explicit solutions for the Satsuma–Hirota coupled equation

2010 ◽  
Vol 216 (9) ◽  
pp. 2628-2634 ◽  
Author(s):  
Xianguo Geng ◽  
Guoliang He
Keyword(s):  
Darboux Transformation ◽  
Explicit Solutions ◽  
Coupled Equation

scholarly journals Characters of Explicit Solutions for a Semidiscrete Integrable Coupled Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Qiulan Zhao ◽  
Qianqian Yang ◽  
Xiangwen Qu
Keyword(s):  
Darboux Transformation ◽  
Coupled System ◽  
Transformation Method ◽  
Explicit Solutions ◽  
Curvature Equation ◽  
Zero Curvature ◽  
Before And After ◽  
Free Function ◽  
Coupled Equation

A semidiscrete integrable coupled system is obtained by embedding a free function into the discrete zero-curvature equation. Then, explicit solutions of the first two nontrivial equations in this system are derived directly by the Darboux transformation method. Finally, in order to compare the solutions before and after coupling intuitively, their structure figures are presented and analyzed.

Explicit Solutions and Conservation Laws of a Coupled Burgers’ Equation

2017 ◽  
Vol 72 (9) ◽  
pp. 789-793
Author(s):  
Bo Xue ◽  
Fang Li ◽  
Yihao Li ◽  
Mingming Sun
Keyword(s):  
Conservation Laws ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Burgers Equation ◽  
Integrable Equation ◽  
Explicit Solutions ◽  
Spectral Problems ◽  
Coupled Burgers Equation

AbstractBased on the gauge transformation between the corresponding 3×3 matrix spectral problems, N-fold Darboux transformation for a coupled Burgers’ equation is constructed. Considering the N=1 case of the derived Darboux transformation, explicit solutions for the coupled Burgers’ equation are given and their figures are plotted. Moreover, conservation laws of this integrable equation are deduced.

scholarly journals N-fold Darboux transformation and explicit solutions in terms of the determinant for the three-field Blaszak–Marciniak lattice

2013 ◽  
Vol 26 (11) ◽  
pp. 1076-1081 ◽  
Author(s):  
Xiao-Yong Wen ◽  
Xiang-Hua Meng ◽  
Xiao-Ge Xu ◽  
Jing-Tao Wang
Keyword(s):  
Darboux Transformation ◽  
Explicit Solutions

DARBOUX TRANSFORMATION AND EXPLICIT SOLUTIONS FOR A 3-FIELD INTEGRABLE LATTICE SYSTEM WITH THREE ARBITRARY CONSTANTS

2011 ◽  
Vol 25 (19) ◽  
pp. 2609-2619 ◽  
Author(s):  
XI-XIANG XU
Keyword(s):  
Darboux Transformation ◽  
Lax Pair ◽  
Lattice System ◽  
Explicit Solutions ◽  
Integrable Lattice ◽  
In Virtue Of

A 3-field integrable lattice system with three arbitrary constants and its Lax pair are presented. In virtue of the Lax pair, a Darboux transformation for the 3-field integrable lattice system is obtained, from which the explicit solutions of the 3-field integrable lattice system are given.

Quasi-Grammian solutions of the generalized Heisenberg magnet model

2020 ◽  
Vol 98 (3) ◽  
pp. 303-311
Author(s):  
Z. Amjad ◽  
B. Haider
Keyword(s):  
Darboux Transformation ◽  
Lie Group ◽  
Soliton Solutions ◽  
Two Dimensions ◽  
Explicit Solutions ◽  
Heisenberg Magnet ◽  
Model Based ◽  
Binary Darboux Transformation

In this paper we use standard binary Darboux transformation to obtain the quasi-Grammian multi-soliton solutions of generalized Heisenberg magnet model in two dimensions. We also discuss the model based on the Lie group SU(n) and obtain explicit solutions of the model for the SU(2) case.

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