21. Januar 2026
Johanna Marstrander (NTNU Trondheim)
Solitary waves for dispersive equations with Coifman-Meyer nonlinearities
This talk concerns the existence of solitary-wave solutions to a class of nonlinear, dispersive evolution equations with Coifman-Meyer nonlinearities. Much effort has been put into answering whether there are solitary-wave solutions to a class of unidirectional, nonlinear wave equations,
ut + (Mu + n(u))x = 0,
which arise in the study of water waves. Here, M is a possibly nonlocal, linear Fourier operator, whereas n is a local, nonlinear function. Inspired by several models where nonlinear frequency interaction appears, we extend the theory to allow for nonlocal nonlinearities in the form of bilinear Fourier multipliers or pseudo-products, N(u,u). We establish the existence of smooth solitary waves to such equations when the linear multiplier is of positive and slightly higher order than the operator on the nonlinear term. The proof is based on a modified version of Weinstein’s argument for L2-constrained minimization using Lions’ method of concentration-compactness.