Rogue Wave Solutions for the Heisenberg Ferromagnet Equations

Zhang, Yan; Nie, Xian-Jia; Zha, Qi-Lao

doi:10.1088/0256-307x/31/6/060201

Cited by 13 publications

(6 citation statements)

References 29 publications

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“…Next, we construct a single Darboux transformation for the generalized Landau-Lifshitz equation with a self-consistent potential [16]. To do this, consider the following transformation of the solutions of the system (3)-( 4)…”

Section: The Darboux Transformationmentioning

confidence: 99%

Soliton solution for the integrable spin model with self-consistent potential

Sagidullayeva

2023

J. Phys.: Conf. Ser.

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Integrable spin systems with potential are of great interest from the point of view of theoretical and applied physics. They make it possible to obtain accurate analytical solutions and study the properties of solitons - nonlinear wave structures that can be stable and move without distortion. The study of solitons in spin systems is of great importance not only for developing new methods for transmitting and processing information but also for developing spintronics and magnetoelectronics in general. These areas of technology are based on the use of the properties and control of the spin moment of electrons. Understanding and controlling spin dynamics in various systems opens up new possibilities for creating more efficient and powerful devices such as magnetic memories, spintronic transistors, and logic elements. This paper considers occurence of soliton in magnetic medium described by Generalized Landau-Lifshitz equation with self-consistent potential.

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Section: The Darboux Transformationmentioning

confidence: 99%

Soliton solution for the integrable spin model with self-consistent potential

Sagidullayeva

2023

J. Phys.: Conf. Ser.

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“…This 'seed' spin is a static field (independent of t) with energy density k 4 0 2 . Recently, Darboux transformation has been constructed starting with a more general seed solution [35,36] for which (20) arises as a special case. A comparative study between classical HF model and the NLSE, in the context of breather (rogue) excitations has also been done recently [37], wherein the space curve formalism has been employed to obtain the curvature and torsion associated with NLSE breather solutions.…”

Section: Exact Recurrence In Classical Hf Spin Chainmentioning

confidence: 99%

Exact and non-exact Fermi–Pasta–Ulam–Tsingou recurrences in a Heisenberg ferromagnet

Ramakrishnan¹,

Murugesh²

2020

Phys. Scr.

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We visualize the Fermi–Pasta–Ulam–Tsingou (FPUT) recurrence in a classical Heisenberg ferromagnetic (HF) spin chain by exploiting its gauge equivalence to the nonlinear Schrödinger equation (NLSE). We discuss two types of spatially periodic breather excitations in the spin chain, that are associated with: (I) Akhmediev breather (AB), and (II) Galilean transformed AB. The recurrence in the former is exact in the sense that the initial and final states are identical. In the later, the spin chain undergoes an additional global rotation during the recurrence process, which makes the initial and final states distinguishable. Both the complex solutions (I) and (II) nevertheless show a definite phase shift during the recurrence process. A one-to-one correspondence between HF spin chain and the NLSE seems missing by virtue of the closeness of the FPUT recurrence.

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“…The whole paper is organized as follows. In section 2, we adopt a hodograph transformation to transform the 2SP equation ( 2) to another nonlinear partial differ ential equation, which is a Lax integrable system belonging to the Heisenberg ferromagnet (HF) hierarchy [44,60]. In section 3, we define a Darboux transformation in terms of the Darboux matrix, and then provide a detailed proof for the Darboux transformation and its quasideterminant representation of the N-fold case.…”

Section: Introductionmentioning

confidence: 99%

Multi-soliton solutions and the Cauchy problem for a two-component short pulse system

Zhaqilao

Zhang

2017

Nonlinearity

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In this paper, we study the Cauchy problem and multi-soliton solutions for a two-component short pulse system. For the Cauchy problem, we first prove the existence and uniqueness of solution with an estimate of the analytic lifespan, and then investigate the continuity of the data-to-solution map in the space of analytic function. For the multi-soliton solutions, we first derive an N -fold Darboux transformation from the Lax pair of the two-component short pulse system, which is expressed in terms of the quasideterminant. Then by virtue of the N -fold Darboux transformation we obtain multi-loop and breather soliton solutions. In particular, one-, two-, three-loop soliton, and breather soliton solutions are discussed in details with interesting dynamical interactions and shown through figures.

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Rogue Wave Solutions for the Heisenberg Ferromagnet Equations

Abstract: Darboux transformation of the Heisenberg ferromagnet equation is constructed by the Darboux matrix method. In application, the rogue wave solutions of the Heisenberg ferromagnet equation are obtained. In particular, rogue waves are discussed and illustrated.

Cited by 13 publications

References 29 publications

Soliton solution for the integrable spin model with self-consistent potential

Soliton solution for the integrable spin model with self-consistent potential

Exact and non-exact Fermi–Pasta–Ulam–Tsingou recurrences in a Heisenberg ferromagnet

Multi-soliton solutions and the Cauchy problem for a two-component short pulse system

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