Integrability and soliton in a classical one-dimensional site-dependent biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity

The integrability of one-dimensional classical continuum inhomogeneous biquadratic Heisenberg spin chain and the effect of nonlinear inhomogeneity on the soliton of an underlying completely integrable spin model are studied. The dynamics of the spin system is expressed in terms of a higher order generalized nonlinear Schrodinger equation through a differential geometric approach which becomes integrable for a particular choice of the biquadratic exchange interaction and for linear inhomogeneity. The effect of nonlinear inhomogeneity on the spin soliton is studied by carrying out a multiple scale perturbation analysis.

[1]  L. Kavitha,et al.  Localized spin excitations in an anisotropic Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions , 2001 .

[2]  K. Porsezian,et al.  On the integrability of the inhomogeneous spherically symmetric Heisenberg ferromagnet in arbitrary dimensions , 1994 .

[3]  L. Kavitha,et al.  SOLITON SPIN EXCITATIONS IN AN ANISOTROPIC HEISENBERG FERROMAGNET WITH OCTUPOLE-DIPOLE INTERACTION , 1999 .

[4]  Paul F. Byrd,et al.  Handbook of elliptic integrals for engineers and scientists , 1971 .

[5]  H. Fogedby.  Solitons and magnons in the classical Heisenberg chain , 1980 .

[6]  M. Ablowitz,et al.  A connection between nonlinear evolution equations and ordinary differential equations of P‐type. II , 1980 .

[7]  M. Lakshmanan,et al.  Geometrical and gauge equivalence of the generalized Hirota, Heisenberg and Wkis equations with linear inhomogeneities , 1985 .

[8]  V. Zakharov,et al.  Equivalence of the nonlinear Schrödinger equation and the equation of a Heisenberg ferromagnet , 1979 .

[9]  Yuji Kodama,et al.  Perturbations of solitons and solitary waves , 1981 .

[10]  Papanicolaou,et al.  Bethe ansatz for two-magnon bound states in anisotropic magnetic chains of arbitrary spin. , 1987, Physical review. B, Condensed matter.

[11]  M. Lakshmanan,et al.  Geometry of generalised nonlinear Schrödinger and Heisenberg ferromagnetic spin equations with linearly x-dependent coefficients , 1980 .

[12]  C. Kittel.  Model of Exchange-Inversion Magnetization , 1960 .

[13]  M. Wadati,et al.  Simple Derivation of Bäcklund Transformation from Riccati Form of Inverse Method , 1975 .

[14]  M. Lakshmanan,et al.  Perturbation of solitons in the classical continuum isotropic Heisenberg spin system , 1983 .

[15]  M. Lakshmanan,et al.  Continuum spin system as an exactly solvable dynamical system , 1977 .

[16]  R. Balakrishnan.  On the inhomogeneous Heisenberg chain , 1982 .

[17]  M. Tabor,et al.  The Painlevé property for partial differential equations , 1983 .

[18]  M. Lakshmanan,et al.  Effect of discreteness on the continuum limit of the Heisenberg spin chain , 1988 .

[19]  和達 三樹.  M. J. Ablowitz and H. Segur: Solitons and the Inverse Scattering Transform, Society for Industrial and Applied Mathematics, Philadelphia, 1981, x+425ページ, 23.5×16.5cm, $54.40 (SIAM Studies in Applied Mathematics). , 1982 .

[20]  M. Ablowitz,et al.  The Inverse scattering transform fourier analysis for nonlinear problems , 1974 .

[21]  M. Daniel,et al.  Generalized χ-dependent Hirota equation: singularity structure, Bäcklund transformation and soliton solutions , 1991 .

[22]  H. Babujian.  Exact solution of the isotropic Heisenberg chain with arbitrary spins: Thermodynamics of the model , 1983 .

[23]  L. Takhtajan.  The picture of low-lying excitations in the isotropic Heisenberg chain of arbitrary spins , 1982 .

[24]  Spin one exchange interaction model of ferromagnetism , 1967 .

[25]  Colin J. Thompson,et al.  On the dynamics of a continuum spin system , 1976 .

[26]  Philip W. Anderson,et al.  New Approach to the Theory of Superexchange Interactions , 1959 .

[27]  M. Lakshmanan,et al.  On the integrability aspects of the one-dimensional classical continuum isotropic biquadratic Heisenberg spin chain , 1992 .

[28]  F. Haldane.  Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State , 1983 .