Abstract
We consider a nonlinear Schrödinger equation with a nonlinearity of the form $V(x)g(u)$. Assuming that $V(x)$ behaves like $|x|^{-b}$ at infinity and $g(s)$ like $|s|^p$ around $0$, we prove the existence and orbital stability of travelling waves if $1 < p < 1+(4-2b)/N$.
Citation
Louis Jeanjean. Stefan Le Coz. "An existence and stability result for standing waves of nonlinear Schrödinger equations." Adv. Differential Equations 11 (7) 813 - 840, 2006. https://doi.org/10.57262/ade/1355867677
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