Periodic weak solutions for a classical one-dimensional isotropic biquadratic Heisenberg spin chain
type: Item
instance of: scholarly article
title: Periodic weak solutions for a classical one-dimensional isotropic biquadratic Heisenberg spin chain
zbMATH Open document ID: 1112.82012
author: Ming Zeng
author: Fengqiu Su
author: Boling Guo
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-04-10T00:00:00Z
review text: In the paper it is considered the equation \[ u_t = u\times u_{xxxx} +\bigg[\bigg( 1+\frac{5}{2}| u_x| ^2\bigg)u\times u_{x}\bigg]_x -\varepsilon u_{xxxx}-\epsilon \bigg(\frac{ 3}{2}| u_x| ^2_{xx} +u_x\cdot u_{xxx}\bigg)u, \] with initial conditions \(u(x, 0) = u_0\), \(u(x + 2D,t) = u(x, t)\), which relates to the one-dimensional isotropic biquadratic Heisenberg spin chain model [see \textit{M. Lakshmanan, K. Porsezian} and \textit{M. Daniel}, Phys. Lett. A 133, 483--488 (1988)]. Following the results of integrability in [\textit{K. Porsezian, M. Daniel} and \textit{M. Lakshmanan}, J. Math. Phys. 33, No. 5, 1807--1816 (1992; Zbl 1112.82309)], the authors prove the existence of weak solution \(u_\varepsilon\) of the above equation. Moreover, the uniform estimates of the solution with respect to \(\varepsilon\) is obtained.
reviewed by: Farruh Mukhamedov
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 35G25
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 5141614
zbMATH Keywords: isotropic biquadratic Heisenberg spin chain
zbMATH Keywords: weak solutions
zbMATH Keywords: viscosity vanishing method
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.08.010
OpenAlex ID: W2028488212
cites work: On the integrability aspects of the one-dimensional classical continuum isotropic biquadratic Heisenberg spin chain
cites work: Q5759616
cites work: Measure-valued solution to the strongly degenerate compressible Heisenberg chain equations
cites work: Existence and uniqueness of smooth solution for system of ferromagnetic chain
cites work: Q5890172
DOI: 10.1016/J.JMAA.2006.08.010
description: scientific article; zbMATH DE number 5141614