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The dynamic properties of a generalized Kawahara equation with Kuramoto-Sivashinsky perturbation

  • * Corresponding author: Zengji Du

    * Corresponding author: Zengji Du 

This work is supported by the Natural Science Foundation of China (Grant Nos. 11871251, 12090011 and 11771185)

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  • In this paper, we are concerned with the existence of solitary waves for a generalized Kawahara equation, which is a model equation describing solitary-wave propagation in media. We obtain some qualitative properties of equilibrium points and existence results of solitary wave solutions for the generalized Kawahara equation without delay and perturbation by employing the phase space analysis. Furthermore the existence of solitary wave solutions for the equation with two types of special delay convolution kernels is proved by combining the geometric singular perturbation theory, invariant manifold theory and Fredholm orthogonality. We also discuss the asymptotic behaviors of traveling wave solutions by means of the asymptotic theory. Finally, some examples are given to illustrate our results.

    Mathematics Subject Classification: 35Q53, 34D15, 34C45.


    \begin{equation} \\ \end{equation}
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  • Figure 1.  The graph of the traveling wave $ \Phi(\xi) $

    Figure 2.  The graph of the traveling wave $ \Phi(\xi) $

    Figure 3.  The graph of the traveling wave $ \Phi(\xi) $

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