Autoresonance excitation of a breather in weak ferromagnetics

Garifullin, R. N.; Kalyakin, L. A.; Шамсутдинов, М. А.

doi:10.1134/s0965542507070081

Cited by 15 publications

(10 citation statements)

References 6 publications

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“…Solitons (or solitary waves) are present in a wide range of physics such as optics [1,2], superconducting Josephson junction arrays [3,4,5], particle and nuclear physics [6,7], condensed matter physics [8,9,10,11,12,13,14,15], and many others [16,17,18,19]. They are robust with respect to small perturbations, they can travel long distances maintaining their shape, and survive collisions with each other.…”

Section: Introductionmentioning

confidence: 99%

Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions

2018

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Abstract. In our recent study the maximal values of kinetic and potential energy densities that can be achieved in the collisions of N slow kinks in the sine-Gordon model were calculated analytically (for N = 1, 2, and 3) and numerically (for 4 ≤ N ≤ 7). However, for many physical applications it is important to know not only the total potential energy density but also its two components (the on-site potential energy density and the elastic strain energy density) as well as the extreme values of the elastic strain, tensile (positive) and compressive (negative). In the present study we give (i) the two components of the potential energy density and (ii) the extreme values of elastic strain. Our results suggest that in multisoliton collisions the main contribution to the potential energy density comes from the elastic strain, but not from the on-site potential. It is also found that tensile strain is usually larger than compressive strain in the core of multi-soliton collision.PACS. 05.45.Yv Solitons -11.10.Lm Nonlinear or nonlocal theories and models -45.50.Tn Collisions

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Section: Introductionmentioning

confidence: 99%

Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions

2018

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“…Such a structure of the equation allows effectively constructing an asymptotic expansion for J(ϕ, I, θ) as θ → ∞ in the form of series (11). The coefficients are uniquely determined by recurrence relations in a class of functions with zero mean, J k (ϕ, I) = 0, because the right-hand side has a zero mean at each step by virtue of (12). The considered problem reduces to integrating over ϕ; the variable I is involved as a parameter in these formulas.…”

Section: Asymptotic Forms Of Oscillating Solutionsmentioning

confidence: 99%

“…Nevertheless, some number of the first corrections are used to calculate the leading-order term of the average I(θ) and to estimate the remainder. It can be concluded from a rough analysis of averaged equation (12) that to identify the nondecreasing terms in the asymptotic expansion of the function I(θ), we must calculate an asymptotic approximation of the right-hand side up to the order O(θ −1 ). Hence, we must calculate oscillating part (11) up to the order O(θ −6/4 ).…”

Section: Asymptotic Forms Of Oscillating Solutionsmentioning

confidence: 99%

“…Indeed, in view of averaged equation (12), the basic equation for action (10) is written as a partial differential equation for the function J(ϕ, I, θ) in three variables. For the following analysis, it is convenient to use the notation F and G given in (8) for some of the summands:…”

Section: Asymptotic Forms Of Oscillating Solutionsmentioning

confidence: 99%

“…As shown in[12], autoresonance is possible with parametric perturbation in a system with small dissipation.…”

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confidence: 97%

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Autoresonant asymptotics in an oscillating system with weak dissipation

Kalyakin

Шамсутдинов

2009

Theor Math Phys

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We study a system of two first-order differential equations arising in averaging nonlinear systems over fast single-frequency oscillations. We consider the situation where the original system contains weak dissipative terms. We construct the asymptotic form of a two-parameter solution with an unbounded increasing amplitude. This result gives a key for understanding autoresonance in weak dissipative systems as a phenomenon of significant increase in the forced nonlinear oscillation initiated by a small external pumping.

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Exact solutions to the sine-Gordon equation

Aktosun

Demontis

Mee

2010

Journal of Mathematical Physics

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A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable x and the temporal variable t, and they are exponentially asymptotic to integer multiples of 2π as x → ±∞. The solution formulas are expressed explicitly in terms of a real triplet of constant matrices. The method presented is generalizable to other integrable evolution equations where the inverse scattering transform is applied via the use of a Marchenko integral equation. By expressing the kernel of that Marchenko equation using a matrix exponential in terms of the matrix triplet and by exploiting the separability of that kernel, an exact solution formula to the Marchenko equation is derived, yielding various equivalent exact solution formulas for the sine-Gordon equation. C

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Autoresonance excitation of a breather in weak ferromagnetics

Cited by 15 publications

References 6 publications

Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions

Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions

Autoresonant asymptotics in an oscillating system with weak dissipation

Exact solutions to the sine-Gordon equation

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