### Abstract

In this paper a globally convergent computational scheme is established to approximate a topological multivortex solution in the recently discovered self-dual Chern-Simons theory in R^{2}. Our method which is constructive and numerically efficient finds the most superconducting solution in the sense that its Higgs field has the largest possible magnitude. The method consists of two steps: first one obtains by a convergent monotone iterative algorithm a suitable solution of the bounded domain equations and then one takes the large domain limit and approximates the full piane solutions. It is shown that with a special choice of the initial guess function, the approximation sequence approaches exponentially fast a solution in R^{2}. The convergence rate implies that the truncation errors away from local regions are insignificant.

Original language | English (US) |
---|---|

Pages (from-to) | 75-97 |

Number of pages | 23 |

Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |

Volume | 12 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2016 |

### Fingerprint

### Keywords

- Monotone iterations
- Sobolev embeddings

### ASJC Scopus subject areas

- Analysis
- Mathematical Physics

### Cite this

**Topological solutions in the self-dual Chern-Simons theory : existence and approximation.** / Spruck, Joel; Yang, Yisong.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Topological solutions in the self-dual Chern-Simons theory

T2 - existence and approximation

AU - Spruck, Joel

AU - Yang, Yisong

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this paper a globally convergent computational scheme is established to approximate a topological multivortex solution in the recently discovered self-dual Chern-Simons theory in R2. Our method which is constructive and numerically efficient finds the most superconducting solution in the sense that its Higgs field has the largest possible magnitude. The method consists of two steps: first one obtains by a convergent monotone iterative algorithm a suitable solution of the bounded domain equations and then one takes the large domain limit and approximates the full piane solutions. It is shown that with a special choice of the initial guess function, the approximation sequence approaches exponentially fast a solution in R2. The convergence rate implies that the truncation errors away from local regions are insignificant.

AB - In this paper a globally convergent computational scheme is established to approximate a topological multivortex solution in the recently discovered self-dual Chern-Simons theory in R2. Our method which is constructive and numerically efficient finds the most superconducting solution in the sense that its Higgs field has the largest possible magnitude. The method consists of two steps: first one obtains by a convergent monotone iterative algorithm a suitable solution of the bounded domain equations and then one takes the large domain limit and approximates the full piane solutions. It is shown that with a special choice of the initial guess function, the approximation sequence approaches exponentially fast a solution in R2. The convergence rate implies that the truncation errors away from local regions are insignificant.

KW - Monotone iterations

KW - Sobolev embeddings

UR - http://www.scopus.com/inward/record.url?scp=85012249208&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85012249208&partnerID=8YFLogxK

U2 - 10.1016/S0294-1449(16)30168-8

DO - 10.1016/S0294-1449(16)30168-8

M3 - Article

VL - 12

SP - 75

EP - 97

JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

SN - 0294-1449

IS - 1

ER -