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1 IPSO - Invariant Preserving SOlvers IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique 2 IRMAR - Institut de Recherche Mathématique de Rennes

Abstract : We consider the approximation of the ground state of the one-dimensional cubic nonlinear Schrödinger equation by a normalized gradient algorithm combined with linearly implicit time integrator, and finite difference space approximation. We show that this method, also called imaginary time evolution method in the physics literature, is con-vergent, and we provide error estimates: the algorithm converges exponentially towards a modified solitons that is a space discretization of the exact soliton, with error estimates depending on the discretization parameters.

Keywords : ground state imaginary time method nonlinear Schroedinger equation





Author: Erwan Faou - Tiphaine Jézéquel -

Source: https://hal.archives-ouvertes.fr/



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