| Citation: |
Jie Song, Jibin Li. BIFURCATIONS AND EXACT TRAVELLING WAVE SOLUTIONS FOR A SHALLOW WATER WAVE MODEL WITH A NON-STATIONARY BOTTOM SURFACE[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 350-360. doi: 10.11948/20190254
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BIFURCATIONS AND EXACT TRAVELLING WAVE SOLUTIONS FOR A SHALLOW WATER WAVE MODEL WITH A NON-STATIONARY BOTTOM SURFACE
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Abstract
We consider a shallow water wave model with a non-stationary bottom surface. By applying dynamical system approach to the model problem, we are able to obtain all possible bounded solutions (compactons, solitary wave solutions and periodic wave solutions) under different parameter conditions. More than 19 exact parametric representations are provided explicitly. -
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References
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Jie Song, Jibin Li. BIFURCATIONS AND EXACT TRAVELLING WAVE SOLUTIONS FOR A SHALLOW WATER WAVE MODEL WITH A NON-STATIONARY BOTTOM SURFACE[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 350-360. doi: 10.11948/20190254
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Figure 1. The bifurcations of phase portraits of system (1.3) when
$ a $ varies -
Figure 2. The changes of the level curves defined by
$ H_{\tilde{a}_-}(\phi,y) = h $ when$ \tilde{a}_- = \frac12(1-\sqrt{5}) $ - Figure 3. The profiles of solitary wave, periodic wave and compactons of equation (1.1)
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Figure 4. The changes of the level curves defined by
$ H_0(\phi,\; y) = h $ when provided$ a = 0 $