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.

Original languageEnglish
Article number111849
JournalNonlinear Analysis, Theory, Methods and Applications
Publication statusPublished - 1 Aug 2020

    Research areas

  • Cubic nonlinearity, Large amplitude waves, Shallow water equation, Well-posedness

ID: 71532245