| Abstract: |
| The talk discusses the exact theory for the existence of single or multi-hump surface waves with small oscillations at infinity on a layer of fluid with finite depth. The fluid is assumed to be incompressible and inviscid with a constant density (one common example is water) and the flow is irrotational. The surface wave is propagating with a constant speed on the free surface under gravity and small surface tension. If the wave speed is near its critical value, it has been shown that the fully nonlinear governing equations, also called the Euler equations, have solitary-wave solutions of elevation with small oscillations at infinity, known as generalized solitary waves. In this talk, the existence of two-hump solutions
with small oscillations at infinity for the Euler equations will be considered. (This is a joint work with S. Deng). |
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