Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonzero boundary conditions
type: Item
instance of: scholarly article
title: Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonzero boundary conditions
zbMATH Open document ID: 1465.35369
DOI: 10.1134/S0040577920120053
author: Jin-Jie Yang
author: Shou-Fu Tian
published in: Theoretical and Mathematical Physics
publication date: 2021-02-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1909.11263
review text: The authors study a matrix Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonvanishing boundary conditions at infinity. Different soliton solutions are sought in a uniaxial ferromagnetic nanowire. The authors introduce an affine transformation which converts the boundary functions into constants, and thus obtain asymptotic Lax pairs. Analytic properties of the scattering matrix are obtained using a spectral analysis. The dynamical behavior of soliton solutions are also studied with reflectionless potentials. Finally, characteristics of the soliton solutions are analyzed graphically, and based on the analytic solutions, the authors propose a method for controlling nonlinear phenomena related to the dynamics of the soliton waves and breather waves.
reviewed by: Eric Stachura
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35Q15
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 81U20
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 7314346
zbMATH Keywords: modified Landau-Lifshitz equation
zbMATH Keywords: matrix Riemann-Hilbert problem
zbMATH Keywords: nonzero boundary condition
zbMATH Keywords: soliton solution
MaRDI profile type: Publication
arXiv ID: 1909.11263
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