Resonant averaging for small solutions of stochastic NLS equations

2013/11/26 by Kuksin, Sergei, Maiocchi, Alberto · 2 citations
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1311.6793

Abstract

We consider the free linear Schrödinger equation on a torus \mathbb T^d, perturbed by a hamiltonian nonlinearity, driven by a random force and damped by a linear damping: u_t -iΔu +iνρ|u|^2q_*u = - νf(-Δ) u + √ν (d)/(d t)∑_{k∈ \mathbb Z^d} b_lβ^k(t)e^{ik⋅ x} . Here u=u(t,x), x∈\mathbb T^d, 0

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