| Citation: |
Shaolong Xie, Xiaochun Hong, Junliang Lu. THE BIFURCATION TRAVELLING WAVES OF A GENERALIZED BROER-KAUP EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 210-226. doi: 10.11948/20190268
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THE BIFURCATION TRAVELLING WAVES OF A GENERALIZED BROER-KAUP EQUATION
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Abstract
In this paper, by using the dynamical system theory and simulation method, we study a generalized Broer-Kaup (gBK) equation. Under different parameter conditions, the travelling wave solutions such as kink wave, periodic blow-up wave, periodic wave and solitary wave are given, and the dynamic characters of these solutions are investigated.-
Keywords:
- Broer-Kaup equation /
- periodic wave /
- periodic blow-up wave /
- solitary wave /
- kink wave
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References
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Shaolong Xie, Xiaochun Hong, Junliang Lu. THE BIFURCATION TRAVELLING WAVES OF A GENERALIZED BROER-KAUP EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 210-226. doi: 10.11948/20190268
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Figure 1. The two unbounded periodic blow-up waves with
$ c\! = \!-\!2 $ ,$ A\! = \!4 $ ,$ B\! = \!4 $ and$ h\! = \!5 $ -
Figure 2. The bounded smooth periodic wave with
$ c\! = \!-\!2 $ ,$ A\! = \!4 $ ,$ B\! = \!4 $ and$ h\! = \!5 $ -
Figure 3. The two bounded smooth solitary waves with
$ A = 4 $ and$ B = 4 $ -
Figure 4. The two unbounded periodic waves with
$ c = 2 $ ,$ A = 1 $ ,$ B = 4 $ and$ h = 90 $ -
Figure 5. The four unbounded kink waves with
$ c = 1 $ ,$ A = 0 $ ,$ B = -1 $ and$ h = 4 $ -
Figure 6. The two bounded kink waves with
$ c\! = \!1 $ ,$ A\! = \!0 $ ,$ B\! = \!-\!1 $ ,$ h\! = \!4 $ and$ \varphi_0\! = \!1 $