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.

N-fold Darboux transformation and conservation laws of the modified Volterra lattice

2018 ◽  
Vol 32 (33) ◽  
pp. 1850409 ◽  
Author(s):  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Yong-Li Sun ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Phenomena ◽  
Explicit Solutions ◽  
Spectral Problems

In this work, we study the modified Volterra lattice. Applying the gauge transformation of the associated [Formula: see text] matrix spectral problems, we establish the N-fold Darboux transformation (DT), and then construct a few explicit solutions in terms of determinants upon using the obtained DT. Moreover, all the results are illustrated by the graphs of the solitonic evolution profiles of the aforementioned solutions. Finally, infinitely many conservation laws for the modified Volterra lattice are proposed. The obtained results of this research might be applied to the research on nonlinear phenomena in physics or engineering areas.

scholarly journals Darboux Transformation and Explicit Solutions for a Generalized Sawada-Kotera Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Guo-Liang He ◽  
Ting Su
Keyword(s):  
Periodic Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Soliton Solutions ◽  
Explicit Solutions ◽  
Rational Solutions ◽  
Lax Pairs ◽  
Spectral Problems

A generalized Sawada-Kotera equation and its Lax pairs are proposed. With the help of the gauge transformation between spectral problems, a Darboux transformation for the generalized SK equation is constructed. As an application of the Darboux transformation, we give some explicit solutions of the generalized SK equation such as the rational solutions, soliton solutions, and periodic solutions.

N-fold Darboux transformation of a six-field integrable lattice system

2021 ◽  
pp. 2150248
Author(s):  
Yanan Qin
Keyword(s):  
Conservation Laws ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Lattice System ◽  
Local Conservation ◽  
Integrable Lattice ◽  
Coupled Equation ◽  
Math Phys

In this paper, we studied a semidiscrete coupled equation, which is integrable in the sense of admitting Lax representations. Proposed first by Vakhnenko in 2006, local conservation laws and one-fold Darboux transformation were presented with different forms, respectively, in O. O. Vakhnenko, J. Phys. Soc. Jpn. 84, 014003 (2015); O. O. Vakhnenko, J. Math. Phys. 56, 033505 (2015); O. O. Vakhnenko, J. Math. Phys. 56, 033505 (2015). On the basis of these results, we principally construct [Formula: see text]-fold Darboux transformation by means of researching gauge transformation of its Lax pair, and work out its explicit multisolutions. Given a set of seed solutions and appropriate parameters, we can calculate two-soliton solutions and plot their figures when [Formula: see text].

N-fold Darboux transformation and exact solutions of the Suris system

2018 ◽  
Vol 32 (09) ◽  
pp. 1850019 ◽  
Author(s):  
Qian Li ◽  
Minghui Liu ◽  
Deng-Shan Wang ◽  
Xiao-Yong Wen
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Lax Pair ◽  
Nonlinear Structures ◽  
Physical Phenomena

In this paper, the N-fold Darboux transformation of the Suris system is established by gauge transformation of the Lax pair. As a result, the N-fold exact solutions of the Suris system are derived in terms of the determinant. It is shown that this system can support certain abundant and peculiar nonlinear structures, which may explain some interesting physical phenomena. Moreover, the infinitely many conservation laws of the Suris system are given.

Sign in / Sign up

Export Citation Format

Share Document