### Abstract

We first construct traveling wave solutions for the Schrödinger map in R
^{2} where m has exactly two vortices at approximately (±1/2ε,0) ε R
^{2} of degree ±1. We use a perturbative approach that gives a complete characterization of the asymptotic behavior of the solutions. With a few modifications, a similar construction yields traveling wave solutions of Schrödinger map equations in higher dimensions.

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

Pages (from-to) | 1585-1621 |

Number of pages | 37 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 63 |

Issue number | 12 |

DOIs | |

State | Published - Dec 2010 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*63*(12), 1585-1621. https://doi.org/10.1002/cpa.20338

**Traveling wave solutions of the Schrödinger map equation.** / Lin, Fang-Hua; Wei, Juncheng.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 63, no. 12, pp. 1585-1621. https://doi.org/10.1002/cpa.20338

}

TY - JOUR

T1 - Traveling wave solutions of the Schrödinger map equation

AU - Lin, Fang-Hua

AU - Wei, Juncheng

PY - 2010/12

Y1 - 2010/12

N2 - We first construct traveling wave solutions for the Schrödinger map in R 2 where m has exactly two vortices at approximately (±1/2ε,0) ε R 2 of degree ±1. We use a perturbative approach that gives a complete characterization of the asymptotic behavior of the solutions. With a few modifications, a similar construction yields traveling wave solutions of Schrödinger map equations in higher dimensions.

AB - We first construct traveling wave solutions for the Schrödinger map in R 2 where m has exactly two vortices at approximately (±1/2ε,0) ε R 2 of degree ±1. We use a perturbative approach that gives a complete characterization of the asymptotic behavior of the solutions. With a few modifications, a similar construction yields traveling wave solutions of Schrödinger map equations in higher dimensions.

UR - http://www.scopus.com/inward/record.url?scp=77958524781&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77958524781&partnerID=8YFLogxK

U2 - 10.1002/cpa.20338

DO - 10.1002/cpa.20338

M3 - Article

AN - SCOPUS:77958524781

VL - 63

SP - 1585

EP - 1621

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 12

ER -