Numerical computation of soliton dynamics for NLS equations in a driving potential

Marco Caliari; Marco Squassina

Numerical computation of soliton dynamics for NLS equations in a driving potential

Marco Caliari, Marco Squassina

University of Verona

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We provide some numerical computations for the soliton dynamics of the nonlinear Schr\"odinger equation with an external potential. After computing the ground state solution r of a related elliptic equation we show that, in the semi-classical regime, the center of mass of the solution with initial datum modelled on r is driven by the solution of a Newtonian type law. Finally, we provide some examples and analyze the numerical errors in the two dimensional case when V is an harmonic potential

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Electronic Journal of Differential Equations
Volume	89
Publication status	Published - 2010

Keywords

Numerical computations NLS equations

Cite this

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title = "Numerical computation of soliton dynamics for NLS equations in a driving potential",

abstract = "We provide some numerical computations for the soliton dynamics of the nonlinear Schr\{"}odinger equation with an external potential. After computing the ground state solution r of a related elliptic equation we show that, in the semi-classical regime, the center of mass of the solution with initial datum modelled on r is driven by the solution of a Newtonian type law. Finally, we provide some examples and analyze the numerical errors in the two dimensional case when V is an harmonic potential",

keywords = "Numerical computations NLS equations, Numerical computations NLS equations",

author = "Marco Caliari and Marco Squassina",

year = "2010",

language = "English",

volume = "89",

pages = "1--12",

journal = "Electronic Journal of Differential Equations",

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TY - JOUR

T1 - Numerical computation of soliton dynamics for NLS equations in a driving potential

AU - Caliari, Marco

AU - Squassina, Marco

PY - 2010

Y1 - 2010

N2 - We provide some numerical computations for the soliton dynamics of the nonlinear Schr\"odinger equation with an external potential. After computing the ground state solution r of a related elliptic equation we show that, in the semi-classical regime, the center of mass of the solution with initial datum modelled on r is driven by the solution of a Newtonian type law. Finally, we provide some examples and analyze the numerical errors in the two dimensional case when V is an harmonic potential

AB - We provide some numerical computations for the soliton dynamics of the nonlinear Schr\"odinger equation with an external potential. After computing the ground state solution r of a related elliptic equation we show that, in the semi-classical regime, the center of mass of the solution with initial datum modelled on r is driven by the solution of a Newtonian type law. Finally, we provide some examples and analyze the numerical errors in the two dimensional case when V is an harmonic potential

KW - Numerical computations NLS equations

UR - http://hdl.handle.net/10807/90746

M3 - Article

SN - 1072-6691

VL - 89

SP - 1

EP - 12

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

ER -

Numerical computation of soliton dynamics for NLS equations in a driving potential

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