Numerical computation of soliton dynamics for NLS equations in a driving potential
We provide numerical computations for the soliton dynamics of the nonlinear Schrodinger 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 datu...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2010-06-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/89/abstr.html |
| _version_ | 1819140642222112768 |
|---|---|
| author | Marco Caliari Marco Squassina |
| author_facet | Marco Caliari Marco Squassina |
| author_sort | Marco Caliari |
| collection | DOAJ |
| description | We provide numerical computations for the soliton dynamics of the nonlinear Schrodinger 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 built upon r is driven by the solution to $ddot x=- abla V(x)$. Finally, we provide examples and analyze the numerical errors in the two dimensional case when V is a harmonic potential. |
| first_indexed | 2024-12-22T11:41:48Z |
| format | Article |
| id | doaj.art-16c6ede9c60b4bf79b555673da88764e |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T11:41:48Z |
| publishDate | 2010-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-16c6ede9c60b4bf79b555673da88764e2022-12-21T18:27:16ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-06-01201089,112Numerical computation of soliton dynamics for NLS equations in a driving potentialMarco CaliariMarco SquassinaWe provide numerical computations for the soliton dynamics of the nonlinear Schrodinger 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 built upon r is driven by the solution to $ddot x=- abla V(x)$. Finally, we provide examples and analyze the numerical errors in the two dimensional case when V is a harmonic potential.http://ejde.math.txstate.edu/Volumes/2010/89/abstr.htmlNonlinear Schrodinger equationsground statessoliton dynamics in an external potentialnumerical computation of ground statessemi-classical limit |
| spellingShingle | Marco Caliari Marco Squassina Numerical computation of soliton dynamics for NLS equations in a driving potential Electronic Journal of Differential Equations Nonlinear Schrodinger equations ground states soliton dynamics in an external potential numerical computation of ground states semi-classical limit |
| title | Numerical computation of soliton dynamics for NLS equations in a driving potential |
| title_full | Numerical computation of soliton dynamics for NLS equations in a driving potential |
| title_fullStr | Numerical computation of soliton dynamics for NLS equations in a driving potential |
| title_full_unstemmed | Numerical computation of soliton dynamics for NLS equations in a driving potential |
| title_short | Numerical computation of soliton dynamics for NLS equations in a driving potential |
| title_sort | numerical computation of soliton dynamics for nls equations in a driving potential |
| topic | Nonlinear Schrodinger equations ground states soliton dynamics in an external potential numerical computation of ground states semi-classical limit |
| url | http://ejde.math.txstate.edu/Volumes/2010/89/abstr.html |
| work_keys_str_mv | AT marcocaliari numericalcomputationofsolitondynamicsfornlsequationsinadrivingpotential AT marcosquassina numericalcomputationofsolitondynamicsfornlsequationsinadrivingpotential |