The Existence of Domain Wall Solutions in Ambj?rn--Nielsen-Olesen Theory

CAO Lei, CHEN Shou-xin,

doi:10.13371/j.cnki.chin.q.j.m.2018.03.001

Chinese Quarterly Journal of Mathematics >

2018 , Vol. 33 >Issue 3: 221 - 232

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.03.001

The Existence of Domain Wall Solutions in Ambj?rn--Nielsen-Olesen Theory

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1. School of Mathematics and Statistics,Henan University2. Institute of Contemporary Mathematics, Henan University

CAO Lei(1991-), female, native of Luoyang, Henan, a Ph.D. student of Henan University, engages in partial di®erential equations and mathematical physics; CHEN Shou-xin(1963-), male, native of Zhumadian. Henan, a professor of Henan University, M.S., engages in partial di®erential equations and mathematical physics.

Accepted date: 2018-07-07

Online published: 2020-10-08

Supported by

Supported by National Natural Science Foundation of China(11471100)；

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Abstract

The Ambj?rn-Nielsen-Olesen(ANO) model arises from field theory, in the limiting BPS state, the ANO model is actually a domain wall model which is a basic construct describing a phase transition between two phases. In this paper, we derive a coupled second-order ordinary differential equations of the domain wall model. Then we establish the existence and uniqueness theorem for the domain solutions by using a dynamical shooting method for the parameter γ = 1, and variational method for the parameter γ > 0 and γ = 1.

Key words： ANO model; domain wall; dynamical shooting method; calculus of variations

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CAO Lei, CHEN Shou-xin, . The Existence of Domain Wall Solutions in Ambj?rn--Nielsen-Olesen Theory[J]. Chinese Quarterly Journal of Mathematics, 2018 , 33(3) : 221 -232 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.03.001

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