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

M. Caliari; Marco Squassina

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

M. Caliari^*
, Marco Squassina

^*Corresponding author

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
Issue number	N/A
Publication status	Published - 2010

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Numerical computations NLS equations

Cite this

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abstract = "We provide some numerical computations for the soliton dynamics of the nonlinear Schr\textbackslash{}{"}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 = "M. Caliari and Marco Squassina",

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AU - Caliari, M.

AU - Squassina, Marco

PY - 2010

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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 - https://publicatt.unicatt.it/handle/10807/90746

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JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

IS - N/A

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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