New Types of Interactions between Solitons of the (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation

2005 ◽  
Vol 60 (10) ◽  
pp. 687-695 ◽  
Author(s):  
Chao-Qing Dai ◽  
Jian-Ping Meng ◽  
Jie-Fang Zhang
Keyword(s):  
Phase Shift ◽  
Balance Method ◽  
Variable Separation ◽  
Pacs 02.30 ◽  
Homogeneous Balance Method ◽  
Variable Separation Approach ◽  
Homogeneous Balance

By means of the extended homogeneous balance method and the variable separation approach, more general variable separation solutions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation are obtained. Based on the variable separation solution and by selecting appropriate functions, new types of interactions between the multi-valued and the single-valued solitons, such as compactonlike semi-foldon and compacton, peakon-like semi-foldon and peakon, and bell-like semi-foldon and dromion, are investigated. Meanwhile, we also discuss the phase shift of these interactions. - PACS: 02.30.Jr, 02.30.Ik

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

Exotic Localized Structures of the (2+1)-Dimensional Nizhnik-Novikov- Veselov System Obtained via the Extended Homogeneous Balance Method

2006 ◽  
Vol 61 (5-6) ◽  
pp. 216-224 ◽  
Author(s):  
Chao-Qing Dai ◽  
Guo-quan Zhou ◽  
Jie-Fang Zhang
Keyword(s):  
Coherent Structures ◽  
Phase Shifts ◽  
Balance Method ◽  
Variable Separation ◽  
Localized Structures ◽  
New Type ◽  
Novel Interactions ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

In this paper, we successfully apply the extended homogeneous balance method (EHBM) to derive a new type of variable separation solutions for the (2+1)-dimensional Nizhnik-Novikov-Veselov system. Novel localized coherent structures about multi-valued functions, i.e., special dromion, special peakon and foldon, and the interactions among them are discussed. Moreover, the explicit phase shifts for all the local excitations offered by the quantity U are given and applied to novel interactions among special dromion, special peakon and foldon in detail. - PACS numbers: 05.45.Yv, 02.30.Jr, 02.03Ik

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

scholarly journals Analytical Solution of the Complex Polymer Equation Systems via the Homogeneous Balance Method

2019 ◽  
pp. 1-8 ◽  
Author(s):  
Aly M. Abourabia ◽  
Yasser A. Eldreeny
Keyword(s):  
Balance Method ◽  
Wave Number ◽  
Physical Situation ◽  
Linear Dispersion ◽  
Normal Dispersion ◽  
Homogeneous Balance Method ◽  
Complex Polymer ◽  
Nonlinearly Elastic ◽  
Good Agreement ◽  
Homogeneous Balance

In this article, we solve analytically the nonlinear Doubly Dispersive Equation (DDE) in (1+1)-D by the homogeneous balance method, introduced to investigate the strain waves propagating in a cylindrical rod in complex polymer systems. The linear dispersion relation plays important role in connecting the frequency of the emitted nonlinear waves with the wave number of the ablating laser beam affecting the polymers with their characteristic parameters. In accordance with the normal dispersion conditions, the resulting solitary wave solutions show the compression characters in the nonlinearly elastic materials namely Polystyrene (PS) and PolyMethylMethAcrylate (PMMA). The ratio between the estimated potential and kinetic energies shows good agreement with the physical situation, and as well in making comparisons with the bell-shaped model conducted in the literature.

A note on the homogeneous balance method

1998 ◽  
Vol 246 (5) ◽  
pp. 403-406 ◽  
Author(s):  
Engui Fan ◽  
Hongqing Zhang
Keyword(s):  
Balance Method ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance
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