| Abstract: |
| Peakons are peaked solitary waves $u=a \exp(-|x-ct|)$ that arise as weak solutions in a large family of nonlinear dispersive wave equations $m_t + f(u,u_x)m +(g(u,u_x)m)_x =0$ where $u$ is the wave amplitude and $m=u-u_{xx}$ is the momentum variable.
In this talk, we study weak kink-type solutions of a similar family of nonlinear dispersive wave equations $m_t + f(u,u_x)m +(g(u,u_x)m)_x + h(u,u_x)=0$. These solutions have the form $u = a (1-\exp(-|x-ct|) {\rm sgn}(x-ct)$. Conditions on the nonlinearities for existence of multi-kink solutions are obtained. |
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