We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation. Furthermore, we establish a novel result concerning the local well-posedness of the corresponding Cauchy problem for space-periodic solutions with initial data from the Sobolev space Hs on the circle for s>3∕2.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 1 Aug 2020|
- Cubic nonlinearity
- Large amplitude waves
- Shallow water equation