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| Traveling Wave Solutions of Some $abcd$-Water Wave Models Describing Small Amplitude, Long Wavelength Gravity Waves on the Surface of Water |
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| KeyWord:Pseudo-peakon, solitary wave, kink and anti-kink wave, compacton family, planar dynamical system, $abcd$-water wave models |
| Author Name | Affiliation | | Jibin Li | School of Mathematical Sciences, Zhejiang Normal University, Jinhua, Zhejing 321004, P. R. China
School of Mathematical Science, Huaqiao University, Quanzhou, Fujian 362021, P. R. China | | Zhilong Shi | Faculty of Architectural Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650500, China |
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| Abstract: |
| For some $abcd$-water wave models describing small amplitude, long wavelength gravity waves on the surface of water, in this paper, by using the method of dynamical systems to analyze corresponding traveling wave systems and find the bifurcations of phase portraits, the dynamical behavior of systems can be derived. Under some given parameter conditions, for a wave component, the existence of periodic wave solutions, solitary wave solutions, kink and anti-kink wave solutions as well as compacton families can be proved. Possible exact explicit parametric representations of the traveling wave solutions are given. |
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