Soliton interaction with slowly varying potentials

Abstract

We study the Gross-Pitaevskii equation with a slowly varying smooth potential, $V(x)=W(hx)$. We show that up to time $\log (1/h)/h$ and errors of size $h^2$ in $H^1$, the solution is a soliton evolving according to the classical dynamics of a natural effective Hamiltonian, $ (ξ^2 + \sech^2 * V (x))/2 $. This provides an improvement ($h\to h^2$) compared to previous works, and is strikingly confirmed by numerical simulations.

References in corpus (2)

• Solitary Wave Dynamics in an External Potential
• Semiclassical Nonlinear Schrodinger equations with potential and focusing initial data

Cited by in corpus (2)

• Stochastic acceleration of solitons for the nonlinear Schrödinger equation
• Effective Dynamics of Solitons in the Presence of Rough Nonlinear Perturbations