ABSTRACT
We consider a three-parameter family of non-linear equations with -order non-linearities. Such a family includes as a particular member the well-known b-equation, which encloses the famous Camassa–Holm equation. For certain choices of the parameters, we establish a global existence result and show a scenario that prevents the wave breaking of solutions. Also, we explore unique continuation properties for some values of the parameters.
Disclosure statement
No potential conflict of interest was reported by the author(s).