Solitons for a nonlinear Schr\"odinger equation with a slowly varying potential

Start: 04/09/2018 - 4:15pm
End  : 04/09/2018 - 5:15pm

Applied Math Seminar

Ivan B Ventura (Cal Poly Pomona)


We study the dynamics of solitary waves for a nonlinear Schr\"odinger equation, with an $L^2$-subcritical power nonlinearity. We show that with an initial condition $\eps \le \sqrt h$ away in $H^1$ from a soliton that, up to time $\sim |\log h|/h$, the solution evolves according to the equations from the effective Hamiltonian up to errors of size $\eps+h^2$. We achieve this result using the methods of Holmer-Zworski and the spectral results of Weinstein.

Emmy Noether Rm Millikan 1021 Pomona College

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