We perturb a linear Schr\"odinger equation with Lam\'epotential with a small positive or negative potential. The newperturbed operator has one or more eigenvalues, at most one ineach spectral gap. We then add a nonlinear term and study thestability of the corresponding nonlinear stationary waves.
Stability of standing waves for NLS with perturbed Lam'e potential / Cuccagna, Scipio. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 223:1(2006), pp. 112-160. [10.1016/j.jde.2005.07.017]
Stability of standing waves for NLS with perturbed Lam'e potential
CUCCAGNA, Scipio
2006
Abstract
We perturb a linear Schr\"odinger equation with Lam\'epotential with a small positive or negative potential. The newperturbed operator has one or more eigenvalues, at most one ineach spectral gap. We then add a nonlinear term and study thestability of the corresponding nonlinear stationary waves.
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