Solitary waves for weakly dispersive equations with inhomogeneous nonlinearities

Ola Maehlen

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arXiv · 1902.05372

Solitary waves for weakly dispersive equations with inhomogeneous nonlinearities

Ola Maehlen

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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 $H^{1+s}$.

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Ola Maehlen. 2019-02-14. Solitary waves for weakly dispersive equations with inhomogeneous nonlinearities. https://arxiv.org/abs/1902.05372

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