SOLITARY TRAVELING WATER WAVES OF MODERATE AMPLITUDE

ANNA GEYER
2012 Journal of Nonlinear Mathematical Physics  
We prove the existence of solitary traveling wave solutions for an equation describing the evolution of the free surface for waves of moderate amplitude in the shallow water regime. This non-linear third order partial differential equation arises as an approximation of the Euler equations, modeling the unidirectional propagation of surface water waves. We give a description of the solitary wave profiles by performing a phase plane analysis and study some qualitative features of the solutions.
doi:10.1142/s1402925112400104 fatcat:glofiqpbrff2fi7kxrw6d6wqdy