Global bifurcation of solitary waves to the Boussinesq $abcd$ system
| Autor: | Robin Ming Chen, Jie Jin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Work (thermodynamics)
Applied Mathematics Mathematical analysis Small amplitude Stagnation point Standing wave Constraint (information theory) Mathematics - Analysis of PDEs FOS: Mathematics Limit (mathematics) Focus (optics) Nonlinear Sciences::Pattern Formation and Solitons Analysis Bifurcation Mathematics Analysis of PDEs (math.AP) |
| Popis: | The Boussinesq $abcd$ system arises in the modeling of long wave small amplitude water waves in a channel, where the four parameters $(a,b,c,d)$ satisfy one constraint. In this paper we focus on the solitary wave solutions to such a system. In particular we work in two parameter regimes where the system does not admit a Hamiltonian structure (corresponding to $b \ne d$). We prove via analytic global bifurcation techniques the existence of solitary waves in such parameter regimes. Some qualitative properties of the solutions are also derived, from which sharp results can be obtained for the global solution curves. Specifically, we first construct solutions bifurcating from the stationary waves, and obtain a global continuous curve of solutions that exhibits a loss of ellipticity in the limit. The second family of solutions bifurcate from the classical Boussinesq supercritical waves. We show that the curve associated to the second class either undergoes a loss of ellipticity in the limit or becomes arbitrarily close to having a stagnation point. 25 pages |
| Databáze: | OpenAIRE |
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