A model equation for water waves. (English) Zbl 0873.35073
The authors present a new model for water waves that is based on a solution of a partial differential equation on the mean free surface. The present formulation is much simpler than the integral equation formulations and the model is not derived as an asymptotic limit. The solutions of the proposed equation are constructed by a Stokes expansion in powers of the amplitude of the wave. Some special cases are studied.
Reviewer: V.A.Sava (Iaşi)
MSC:
35Q35 | PDEs in connection with fluid mechanics |
76B65 | Rossby waves (MSC2010) |