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Weak Solutions of a Generalized Boussinesq System

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Abstract

We study the convergence of homoclinic orbits and heteroclinic orbits in the dynamical system governing traveling wave solutions of a perturbed Boussinesq systems modeling two-directional propagation of water waves. Nonanalytic weak solutions are found to be limits of these orbits, including compactons, peakons, and rampons, as well as infinitely many mesaons occurring at the same fixed point in the dynamical system. Singularities of solitary wave solutions in the system are also studied to understand the important impact of both linear and nonlinear dispersion terms on the regularity of these solutions.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Minneapolis, Minnesota, 55455

    Y. A. Li

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  1. Y. A. Li
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Li, Y.A. Weak Solutions of a Generalized Boussinesq System. Journal of Dynamics and Differential Equations 11, 625–669 (1999). https://doi.org/10.1023/A:1022611428785

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