Existence theorems for periodic non-relativistic Maxwell-Chern-Simons solitons

Joel Spruck; Yisong Yang

doi:10.1006/jdeq.1996.0084

Existence theorems for periodic non-relativistic Maxwell-Chern-Simons solitons

Joel Spruck, Yisong Yang

Mathematics

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

Abstract

We study the system of elliptic equations ΔS = μ₁S + K₁e^v, Δv = μ₂S + K₂e^v + K₃, defined over a doubly-periodic domain in R², where the coefficients are specifically given by the physical model. This system arises in a self-dual non-relativistic Maxwell-Chern-Simons theory coupled with a neutral scalar field in (2 + 1)-dimensional spacetime and the solutions represent multivortices known as condensates. Our existence results reveal that the number of vortices confined in a periodic cell domain can be arbitrary and that the Chern-Simons coupling parameter imposes no restriction to the existence of solutions.

Original language	English (US)
Pages (from-to)	571-589
Number of pages	19
Journal	Journal of Differential Equations
Volume	127
Issue number	2
DOIs	https://doi.org/10.1006/jdeq.1996.0084
State	Published - May 20 1996

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "Existence theorems for periodic non-relativistic Maxwell-Chern-Simons solitons",

abstract = "We study the system of elliptic equations ΔS = μ1S + K1ev, Δv = μ2S + K2ev + K3, defined over a doubly-periodic domain in R2, where the coefficients are specifically given by the physical model. This system arises in a self-dual non-relativistic Maxwell-Chern-Simons theory coupled with a neutral scalar field in (2 + 1)-dimensional spacetime and the solutions represent multivortices known as condensates. Our existence results reveal that the number of vortices confined in a periodic cell domain can be arbitrary and that the Chern-Simons coupling parameter imposes no restriction to the existence of solutions.",

author = "Joel Spruck and Yisong Yang",

note = "Funding Information: * Research supported in part by NSF Grant DMS-9403918. -Research supported in part by NSF Grant DMS-9304580 at the Institute for Advanced Study.",

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PY - 1996/5/20

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N2 - We study the system of elliptic equations ΔS = μ1S + K1ev, Δv = μ2S + K2ev + K3, defined over a doubly-periodic domain in R2, where the coefficients are specifically given by the physical model. This system arises in a self-dual non-relativistic Maxwell-Chern-Simons theory coupled with a neutral scalar field in (2 + 1)-dimensional spacetime and the solutions represent multivortices known as condensates. Our existence results reveal that the number of vortices confined in a periodic cell domain can be arbitrary and that the Chern-Simons coupling parameter imposes no restriction to the existence of solutions.

AB - We study the system of elliptic equations ΔS = μ1S + K1ev, Δv = μ2S + K2ev + K3, defined over a doubly-periodic domain in R2, where the coefficients are specifically given by the physical model. This system arises in a self-dual non-relativistic Maxwell-Chern-Simons theory coupled with a neutral scalar field in (2 + 1)-dimensional spacetime and the solutions represent multivortices known as condensates. Our existence results reveal that the number of vortices confined in a periodic cell domain can be arbitrary and that the Chern-Simons coupling parameter imposes no restriction to the existence of solutions.

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Existence theorems for periodic non-relativistic Maxwell-Chern-Simons solitons

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