On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type
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 near the origin; this class includes in particular the Whitham equation. A family of solitary-wave solutions is found using a constrained minimization principle and concentration-compactness methods for noncoercive functionals. T