On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type

Mats Ehrnström, Mark D. Groves, Erik Wahlén

We consider a class of pseudodifferential evolution equations of the form $$u_t+(n(u)+Lu{)}_x=0,$$ in which $L$ is a linear smoothing operator and $n$ is at least quadratic nea…