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On the integrability aspects of the one-dimensional classical continuum isotropic biquadratic Heisenberg spin chain
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In this article, the integrability aspects of a classical one-dimensional continuum isotropic biquadratic Heisenberg spin chain in its continuum limit up to order [O(a4)] in the lattice parameter "a" are studied.Abstract:
The integrability aspects of a classical one‐dimensional continuum isotropic biquadratic Heisenberg spin chain in its continuum limit up to order [O(a4)] in the lattice parameter ‘‘a’’ are studied. Through a differential geometric approach, the dynamical equation for the spin chain is expressed in the form of a higher‐order generalized nonlinear Schrodinger equation (GNLSE). An integrable biquadratic chain that is a deformation of the lower‐order continuum isotropic spin chain, is identified by carrying out a Painleve singularity structure analysis on the GNLSE (also through gauge analysis) and its properties are discussed briefly. For the nonintegrable chain, the perturbed soliton solution is obtained through a multiple scale analysis.read more
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The fascinating world of the Landau-Lifshitz-Gilbert equation: an overview
TL;DR: An exciting recent development is that the spin torque effect in nanoferromagnets is described by a generalization of the LLG equation that forms a basic dynamical equation in the field of spintronics.
Journal ArticleDOI
An elementary geometric characterization of the integrable motions of a curve
Adam Doliwa,Paolo Maria Santini +1 more
TL;DR: In this article, it was shown that the motion of a curve selects hierarchies of integrable dynamics, such as the Korteweg-de Vries hierarchy, the Schrodinger hierarchy, and the Schroff hierarchy.
Journal ArticleDOI
The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview
TL;DR: The spin torque effect in nanoferromagnets is described by a generalization of the Landau-Lifshitz-Gilbert (LLG) equation which forms a basic dynamical equation in the field of spintronics as discussed by the authors.
Journal ArticleDOI
Soliton spin excitations in an anisotropic Heisenberg ferromagnet with octupole-dipole interaction
M. K. Daniel,L. Kavitha,R. Amuda +2 more
TL;DR: In this paper, the nonlinear spin dynamics of an anisotropic Heisenberg ferromagnetic spin chain with octupole-dipole interaction in the semiclassical limit using the coherent-state method combined with the Holstein-Primakoff bosonic representation of spin operators were investigated.
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Darboux transformations and rogue wave solutions of a generalized AB system for the geophysical flows
TL;DR: A generalized AB system, which is used to describe certain baroclinic instability processes in the geophysical flows, is investigated, and the Darboux and generalizedDarboux transformations are derived, both relevant to the coefficient of the nonlinear term and coefficient related to the shear.
References
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Book
Solitons and the Inverse Scattering Transform
Mark J. Ablowitz,Harvey Segur +1 more
TL;DR: In this paper, the authors developed the theory of the inverse scattering transform (IST) for ocean wave evolution, which can be solved exactly by the soliton solution of the Korteweg-deVries equation.
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The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
Journal ArticleDOI
The Painlevé property for partial differential equations
TL;DR: In this paper, the authors define the Painleve property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Backlund transforms, the linearizing transforms, and the Lax pairs of three well-known partial differential equation (Burgers' equation, KdV equation, and modified KDV equation).
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A connection between nonlinear evolution equations and ordinary differential equations of P‐type. II
TL;DR: The connection between nonlinear partial differential equations solvable by inverse scattering transforms and nonlinear ODEs of P-type (i.e., no movable critical points) is discussed in this article.
Journal ArticleDOI
Model for a multicomponent quantum system
TL;DR: In this paper, the authors generalize Lai's model to higher-spin systems and a lattice of SU(3) triplets, making application to various systems such as dilute Heisenberg magnets.