Solitary waves and nonlinear dynamic coherent structures in magnetic metamaterials

Tankeyev, A. P.; Smagin, V. V.; Borich, M. A.; Журавлев, А. С.

doi:10.1134/s0031918x0903003x

Cited by 9 publications

(10 citation statements)

References 6 publications

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“…( 88) also admits four superposed periodic kink and pulse solutions. Further, as shown already [2], unlike the symmetric φ 4 case, the MKdV Eq. ( 88) also admits a superposed (hyperbolic) kink solution.…”

Section: Novel Superposed Solutions Of Mkdv Equationsupporting

confidence: 55%

“…In Sec. IV we discuss the MKdV equation and show that apart from the superposed hyperbolic kink solution already known [2], like the symmetric φ 4 case, the MKdV equation also admits superposed periodic kink and pulse solutions. Further, using the celebrated Miura transformation [8], from the superposed solutions of the repulsive MKdV equation we immediately obtain the corresponding superposed solutions of the KdV equation.…”

Section: Introductionmentioning

confidence: 84%

“…We now show that the MKdV equation also admits superposed periodic kink and pulse solutions in addition to the superposed hyperbolic kink solution obtained in [2]. Before we do that it is worthwhile reminding about the well known periodic kink and pulse solutions of the MKdV equation [1]…”

Section: Novel Superposed Solutions Of Mkdv Equationmentioning

confidence: 91%

“…Several years ago, in a largely unnoticed paper, Tankeyev, Smagin, Borich and Zhuravlev [2] obtained a novel superposed hyperbolic kink solution for the repulsive MKdV equation. Their work was inspired by the earlier work of [3].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Novel Superposed Kink and Pulse Solutions for $ϕ^4$, MKdV, NLS and Other Nonlinear Equations

Khare¹,

Saxena²

2022

Preprint

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We show that a number of nonlinear equations including symmetric as well as asymmetric φ 4 , modified Korteweg de Vries (MKdV), mixed KdV-MKdV, nonlinear Schrödinger (NLS), quadratic-cubic NLS as well as higher order neutral scalar field theories, higher order KdV-MKdV and higher order quadratic-cubic NLS admit superposed periodic kink and pulse solutions and some of them also admit superposed hyperbolic kink solutions.

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Section: Novel Superposed Solutions Of Mkdv Equationsupporting

confidence: 55%

Section: Introductionmentioning

confidence: 84%

Section: Novel Superposed Solutions Of Mkdv Equationmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Novel Superposed Kink and Pulse Solutions for $ϕ^4$, MKdV, NLS and Other Nonlinear Equations

Khare¹,

Saxena²

2022

Preprint

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“…Applications of the periodic breather modes to various continuous media have been discussed in Refs. [46][47][48][49] . The BL solution has been predicted for continuous β-Fermi-Pasta-Ulam (FPU) chain 50 , finding periodic DB configurations in a triangular β-FPU lattice has been recently reported 51 .…”

Section: Introductionmentioning

confidence: 99%

Dark discrete breather modes in monoaxial chiral helimagnet with easy-plane anisotropy

Bostrem,

Ekomasov,

Kishine

et al. 2021

Preprint

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Nonlinearity and discreteness are two pivotal factors for an emergence of discrete breather excitations in various media. We argue that these requirements are met in the forced ferromagnetic phase of the monoaxial chiral helimagnet CrNb3S6 due to specific domain structure of the compound. The stationary, time-periodic breather modes appear as the discrete breather lattice solutions whose period mismatches with a system size. Thanks to easy-plane single-ion anisotropy intrinsic to CrNb3S6, these modes are of the dark type with frequencies lying within the linear spin-wave band, close to its bottom edge. They represent cnoidal states of magnetization, similar to the well-known soliton lattice ground state, with differing but limited number of embedded 2π-kinks. Linear stability of these dark breather modes is verified by means of the Floquet analysis. Their energy controlled by two parameters, namely the breather lattice period and amplitude, falls off linearly with a growth of the kink number. These results may pave a new path to design spintronic resonators on the base of chiral helimagnets.

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Coupled superposed solutions in nonlinear nonlocal equations

Khare

Saxena

2023

Annals of Physics

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Solitary waves and nonlinear dynamic coherent structures in magnetic metamaterials

Cited by 9 publications

References 6 publications

Novel Superposed Kink and Pulse Solutions for $ϕ^4$, MKdV, NLS and Other Nonlinear Equations

Novel Superposed Kink and Pulse Solutions for $ϕ^4$, MKdV, NLS and Other Nonlinear Equations

Dark discrete breather modes in monoaxial chiral helimagnet with easy-plane anisotropy

Coupled superposed solutions in nonlinear nonlocal equations

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