Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics

1996 ◽  
Vol 216 (1-5) ◽  
pp. 67-75 ◽  
Author(s):  
Mingliang Wang ◽  
Yubin Zhou ◽  
Zhibin Li
Keyword(s):  
Exact Solutions ◽  
Nonlinear Equations ◽  
Mathematical Physics ◽  
Balance Method ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

On The Initial Value Problem And Exact Solutions For The Higher-Order Broer-Kaup Equations

2003 ◽  
Vol 58 (7-8) ◽  
pp. 397-403 ◽  
Author(s):  
Chenglin Bai
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Nonlinear Equations ◽  
Initial Value Problem ◽  
Bäcklund Transformation ◽  
Higher Order ◽  
Balance Method ◽  
Initial Value ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

The Backlund transformation and exact solutions, especially the closed form of the solution for the initial value problem of the higher order Broer-Kaup (BK) systems in (1+1) and (2+1) dimensions, are obtained by using the extended homogeneous balance method. The method used here is simple and can be generalized to deal with other classes of nonlinear equations.

Auto-B¨Acklund Transformations And Exact Solutions For The Generalized Two-Dimensional Korteweg-De Vries-Burgers-Type Equations And Burgers-Type Equations

2003 ◽  
Vol 58 (7-8) ◽  
pp. 464-472
Author(s):  
Biao Li ◽  
Yong Chen ◽  
Hongqing Zhang
Keyword(s):  
Exact Solutions ◽  
Bäcklund Transformation ◽  
Type Equation ◽  
Balance Method ◽  
Two Dimensional ◽  
Backlund Transformation ◽  
De Vries ◽  
Homogeneous Balance Method ◽  
Burgers Type Equations ◽  
Homogeneous Balance

In this paper, based on the idea of the homogeneous balance method and with the help of Mathematica, we obtain a new auto-Bäcklund transformation for the generalized two-dimensional Kortewegde Vries-Burgers-type equation and a new auto-Bäcklund transformation for the generalized twodimensional Burgers-type equation by introducing two appropriate transformations. Then, based on these two auto-Bäcklund transformation, some exact solutions for these equations are derived. Some figures are given to show the properties of the solutions.

scholarly journals Analytical solution of Balitsky-Kovchegov equation with homogeneous balance method

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Xiaopeng Wang ◽  
Yirui Yang ◽  
Wei Kou ◽  
Rong Wang ◽  
Xurong Chen
Keyword(s):  
Analytical Solution ◽  
Balance Method ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

A New Class of (2+1)-Dimensional Combined Structures with Completely Elastic and Non-Elastic Interactive Properties

2006 ◽  
Vol 61 (1-2) ◽  
pp. 53-59 ◽  
Author(s):  
Cheng-Lin Bai ◽  
Cheng-Jie Bai ◽  
Hong Zhao
Keyword(s):  
Solitary Waves ◽  
Balance Method ◽  
Physical Models ◽  
Variable Separation ◽  
New Class ◽  
Localized Structures ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

Taking the new (2+1)-dimensional generalized Broer-Kaup system as an example, we obtain an exact variable separation excitation which can describe some quite universal (2+1)-dimensional physical models, with the help of the extended homogeneous balance method. Based on the derived excitation, a new class of combined structures, i. e., semifolded solitary waves and semifoldons, is defined and studied. The interactions of the semifolded localized structures are illustrated both analytically and graphically. - PACS numbers: 05.45.Yv, 02.30.Jr, 02.30.Ik

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