| Abstract: |
| The generalized Korteweg-de-Vries equation (gKdV) $u_t+ u^p u_x + u_{xxx}=0$ with nonlinearity power $p\geq1$ arises in numerous physical models and its solitary wave solutions have been studied extensively. In this talk, we study its more general travelling wave solutions on a non-zero background. These solutions include solitary waves with non-zero boundary conditions, kink waves, and heavy-tailed waves that exhibit a polynomial decay (rather than exponential decay). We classify all possible types of solutions for general $p$ and derive explicit expressions when $p=1,2,3,4$. |
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