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- W2556970012 abstract "In this paper, we investigate the bifurcations of nonlinear waves described by the Gardner equation $u_{t}+a u u_{x}+b u^{2} u_{x}+gamma u_{xxx}=0$. We obtain some new results as follows: For arbitrary given parameters $b$ and $gamma$, we choose the parameter $a$ as bifurcation parameter. Through the phase analysis and explicit expressions of some nonlinear waves, we reveal two kinds of important bifurcation phenomena. The first phenomenonis that the solitary waves with fractional expressions can be bifurcated from three types of nonlinear waves which are solitary waves with hyperbolic expression and two types of periodic waves with elliptic expression and trigonometric expression respectively. The second phenomenon is that the kink waves can be bifurcated from the solitary waves and the singular waves." @default.
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- W2556970012 date "2016-11-01" @default.
- W2556970012 modified "2023-10-13" @default.
- W2556970012 title "The bifurcations of solitary and kink waves described by the Gardner equation" @default.
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- W2556970012 doi "https://doi.org/10.3934/dcdss.2016067" @default.
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