Viktor Pavlovich Silin (In honor of his 80th birthday)

Aliev, Yu. M.; Andreev, N. E.; Anosova, L. M.; Arsenin, V. V.; Vagin, K. Yu.; Grebenshchikov, S. E.; Gorbunov, L. M.; Malishevskiĭ, A. R.; Ovchinnikov, K. N.; Ramazashvili, Revaz; Romanov, A. Yu.; Rukhadze, A. A.; Тимофеев, А. В.; Uryupin, S. A.; Фролов, Алексей Анатольевич

doi:10.1134/s1063780x06080071

Cited by 3 publications

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“…Our study of some other models of this kind (e.g. various nonlocal generalizations of double and triple sine-Gordon model) also confirms the asymptotical formula (6).…”

Section: Example 2 the Double Sine-gordon Equationsupporting

confidence: 82%

“…where a > 0 is a parameter. In particular, this equation arises in nonlocal Josephson electrodynamics where it describes layered structures [6] (the second sine harmonic is important if they include, for instance, ferromagnetic layers, [11]). A list of possible kernels K ε which arises in Josephson models can be found in [12].…”

Section: Example 2 the Double Sine-gordon Equationmentioning

confidence: 99%

“…It is known that in many dispersive systems the presence of these nonlinear entities is strongly restricted due to resonances with linear excitations. These resonances take place in Hamiltonian systems of various origin, such as the fifth-order Korteweg-de Vries equation [1], nonlinear lattices [2][3][4] and models with complex dispersion and nonlocal interactions [5,6]. As a result, it is quite typical that in such Hamiltonian systems the localized excitations either do not exist at all or they only exist for specific values of some external parameters.…”

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confidence: 99%

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Wave Systems with an Infinite Number of Localized Traveling Waves

2014

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In many wave systems, propagation of steadily traveling solitons or kinks is prohibited because of resonances with linear excitations. We show that wave systems with resonances may admit an infinite number of traveling solitons or kinks if the closest to the real axis singularities of a limiting asymptotic solution in the complex upper half plane are of the form z±=±α+iβ, α≠0. This quite general statement is illustrated by examples of the fifth-order Korteweg-de Vries equation, the discrete cubic-quintic Klein-Gordon equation, and the nonlocal double sine-Gordon equations.

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“…Our study of some other models of this kind (e.g. various nonlocal generalizations of double and triple sine-Gordon model) also confirms the asymptotical formula (6).…”

Section: Example 2 the Double Sine-gordon Equationsupporting

confidence: 82%

Section: Example 2 the Double Sine-gordon Equationmentioning

confidence: 99%

mentioning

confidence: 99%

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Wave Systems with an Infinite Number of Localized Traveling Waves

2014

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“…( 37) is one of the basic model equations. Let's note that some exact solutions of this equation have been found and their stability under weak perturbations has been analyzed [35]- [37].…”

Section: Classical Nonlinear Lattice Dynamicsmentioning

confidence: 99%

Nonlinear fractional dynamics on a lattice with long range interactions

Laskin

Zaslavsky

2006

Physica A: Statistical Mechanics and its Applications

118

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A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. A classical case is treated in the framework of the generalization of the well-known Frenkel-Kontorova chain model for the non-nearest interactions. Quantum dynamics is considered following Davydov's approach for molecular excitons.In the continuum limit the problem is reduced to dynamical equations with fractional derivatives resulting from the fractional power of the long-range interaction. Fractional generalizations of the sine-Gordon, nonlinear Schrödinger, and Hilbert-Schrödinger equations have been found.There exists a critical value of the power s of the long-range potential. Below the critical value (s < 3, s = 1, 2) we obtain equations with fractional derivatives while for s ≥ 3 we have the well-known nonlinear dynamical equations with space derivatives of integer order.Long-range interaction impact on the quantum lattice propagator has been studied. We have shown that the quantum exciton propagator exhibits transition from the well-known Gaussian-like behavior to a power-law decay due to the long-range interaction. A link between 1D quantum lattice dynamics in the imaginary time domain and a random walk model has been discussed.PACS number (s): 03.65.-w, 03.65. Db, 05.30.-d, 05.40. Fb

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“…is fulfilled in the focusing phase of the wakefield [6,13]. This last condition is an important restriction for the realization of this injection scheme and can be satisfied if the wake wave is nonlinear, or/and is excited in the plasma channel, where the accelerating and focusing phases of the wave are overlapped deeper than in the linear plasma wave [15][16][17]. One of the most attractive features of this injection scheme is the possibility to use longer electron bunches due to their strong compression in the process of trapping [6,[12][13][14].…”

Section: Electron Bunch Compression and Monoenergetic Acceleration By...mentioning

confidence: 99%

Laser wakefield acceleration of supershort electron bunches in guiding structures

Andreev¹,

Kuznetsov²,

Cros³

et al. 2010

Plasma Phys. Control. Fusion

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High gradient acceleration of electrons by plasma waves generated in plasma channels by short intense laser pulses is analyzed. The influence of loading effect and initial emittance on the quality of accelerated electron bunches is studied for the proposed scheme of bunch injection in front of a laser pulse, which opens an opportunity for monoenergetic acceleration of ultra-short electron bunches of submicrometer sizes to high energies.

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Viktor Pavlovich Silin (In honor of his 80th birthday)

Cited by 3 publications

References 0 publications

Wave Systems with an Infinite Number of Localized Traveling Waves

Wave Systems with an Infinite Number of Localized Traveling Waves

Nonlinear fractional dynamics on a lattice with long range interactions

Laser wakefield acceleration of supershort electron bunches in guiding structures

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