Exact traveling wave solutions and \(L^{1}\) stability for the shallow water wave model of moderate amplitude. (English) Zbl 1378.35068
Summary: In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in \(L^{1}(\mathbb R)\) space for the Cauchy problem of the equation.
MSC:
| 35C07 | Traveling wave solutions |
| 35G25 | Initial value problems for nonlinear higher-order PDEs |
| 35C05 | Solutions to PDEs in closed form |
| 35B35 | Stability in context of PDEs |
| 35C08 | Soliton solutions |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 35D30 | Weak solutions to PDEs |
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