Painlevé Property, Bäcklund Transformations and Rouge Wave Solutions of (3 + 1)-Dimensional Burgers Equation

2014 ◽  
Vol 61 (6) ◽  
pp. 663-668 ◽  
Author(s):  
Man Jia ◽  
Qing-Xing Zeng ◽  
Zhang Xiao
Keyword(s):  
Burgers Equation ◽  
Bäcklund Transformations ◽  
Wave Solutions ◽  
Painlevé Property ◽  
Backlund Transformations ◽  
Rouge Wave

scholarly journals Painlevé analysis and exact solutions of bosonized N = 1 supersymmetric Burgers equation

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Bo Ren
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Expansion Method ◽  
Singularity Analysis ◽  
Bäcklund Transformations ◽  
Painlevé Analysis ◽  
Explicit Solutions ◽  
Bosonic System ◽  
Painlevé Property ◽  
Backlund Transformations

AbstractBased on the bosonization approach, the N = 1 supersymmetric Burgers (SB) system is transformed to a coupled pure bosonic system. The Painlevé property and the Bäcklund transformations (BT) of the bosonized SB (BSB) system are obtained through standard singularity analysis. Explicit solutions such as the muti-solitarywaves and error functionwaves are provided for the BT. The exact solutions of the BSB system are obtained from the generalized tanh expansion method.

Bäcklund transformations for nonlinear parabolic equations: the general results

1982 ◽  
Vol 384 (1787) ◽  
pp. 381-401 ◽  
Keyword(s):  
Nonlinear Equations ◽  
Parabolic Equations ◽  
Burgers Equation ◽  
Nonlinear Parabolic Equations ◽  
Bäcklund Transformations ◽  
Forcing Term ◽  
Nonlinear Parabolic ◽  
Backlund Transformations

Bäcklund transformations (BTs) are considered for nonlinear parabolic equations of the form u t + u xx + H ( u x , u, x, t ) = 0. (*) The most general form of both the BT and the class (*) is adopted, and we show that the only nonlinear equations (*) possessing BTs are the slight generalizations of Burgers’ equation obtained by adding a forcing term, u t + u xx + 2 uu x + a ( x, t ) = 0.

Bäcklund transformations, Lax pair and solutions of a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves

2021 ◽  
Author(s):  
Tian-Yu Zhou ◽  
Bo Tian ◽  
Su-Su Chen ◽  
Cheng-Cheng Wei ◽  
Yu-Qi Chen
Keyword(s):  
Burgers Equation ◽  
Bäcklund Transformation ◽  
Lax Pair ◽  
Ocean Dynamics ◽  
Bäcklund Transformations ◽  
Backlund Transformation ◽  
Dispersive Waves ◽  
Backlund Transformations ◽  
Hybrid Solutions ◽  
Kink Waves

Burgers-type equations are considered as the models of certain phenomena in plasma astrophysics, ocean dynamics, atmospheric science and so on. In this paper, a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves is studied. Based on the Painlevé-Bäcklund equations, one auto-Bäcklund transformation and two hetero-Bäcklund transformations are derived. Motivated by the Burgers hierarchy, a Lax pair is given. Via two hetero-Bäcklund transformations with different constant seed solutions, we find some multiple-kink solutions, complex periodic solutions, hybrid solutions composed of the lump, periodic and multiple kink waves. Then we discuss the influence of the coefficients of the above equation on such solutions. Via the auto-Bäcklund transformation with the nontrivial seed solutions, we obtain certain lump-type solutions, kink-type solutions and recurrence relation of the above equation.

scholarly journals Bäcklund transformations for the Burgers equation via localization of residual symmetries

2014 ◽  
Vol 23 (11) ◽  
pp. 110203 ◽  
Author(s):  
Xi-Zhong Liu ◽  
Jun Yu ◽  
Bo Ren ◽  
Jian-Rong Yang
Keyword(s):  
Burgers Equation ◽  
Bäcklund Transformations ◽  
Backlund Transformations
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