Slow soliton interaction with delta impurities

Abstract

We study the Gross-Pitaevskii equation with a delta function potential, $q{\delta }_0$, where $|q|$ is small, and analyze the solutions for which the initial condition is a soliton with initial velocity $v_0$. We show that up to time $(|q|+v_0^2{)}^{-\frac{1}{2}}\log (1/|q|)$ the bulk of the solution is a soliton evolving according to the classical dynamics of a natural effective Hamiltonian, $ (ξ^2 + q \sech^2 (x))/2 $.

References in corpus (1)

• Solitary Wave Dynamics in an External Potential

Cited by in corpus (2)

• Stability of two soliton collision for nonintegrable gKdV equations
• Effective Dynamics of Solitons in the Presence of Rough Nonlinear Perturbations