2000 character limit reached
Solitary waves for weakly dispersive equations with inhomogeneous nonlinearities (1902.05372v2)
Published 14 Feb 2019 in math.AP
Abstract: We show existence of solitary-wave solutions to the equation \begin{equation*} u_t+ (Lu - n(u))_x = 0\,, \end{equation*} for weak assumptions on the dispersion $L$ and the nonlinearity $n$. The symbol $m$ of the Fourier multiplier $L$ is allowed to be of low positive order ($s > 0$), while $n$ need only be locally Lipschitz and asymptotically homogeneous at zero. We shall discover such solutions in Sobolev spaces contained in $H{1+s}$.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
