Showing papers by "Yuri S. Kivshar published in 1992"
TL;DR: Numerical simulations show the validity of the analytical approach for the initial stage of the time evolution, provided that the harmonics generated by the nonlinear terms are considered.
Abstract: We study analytically and numerically modulational instabilities in discrete nonlinear chains, taking the discrete Klein-Gordon model as an example. We show that discreteness can drastically change the conditions for modulational instability; e.g., at small wave numbers a nonlinear carrier wave is unstable to all possible modulations of its amplitude if the wave amplitude exceeds a certain threshold value. Numerical simulations show the validity of the analytical approach for the initial stage of the time evolution, provided that the harmonics generated by the nonlinear terms are considered. The long-term evolution exhibits chaoticlike states.
321 citations
TL;DR: It is demonstrated that the SG kink may be totally reflected by an attractive impurity if its initial velocity is in some resonance windows and this effect can be predicted by a suitable collective-coordinate method and the resonance structures can be explained with an energy exchange between the kink translational mode and the impurity mode.
Abstract: We present results concerning kink-impurity interactions in the sine-Gordon (SG) model. In particular, we demonstrate that the SG kink may be totally reflected by an attractive impurity if its initial velocity is in some resonance windows. This effect can be predicted by a suitable collective-coordinate method, and the resonance structures can be explained with an energy exchange between the kink translational mode and the impurity mode. We also study the scattering of the kink by an excited impurity and show that such a scattering strongly depends on the amplitude and phase of the impurity mode. In particular, resonance phenomena are also observed in the scattering. In addition, we consider the interactions of the kink with an isotopic (heavy-mass) impurity. We demonstrate that if the impurity mass is not too large in comparison with the standard mass in the SG model, the kink can pass the impurity almost freely at any initial velocity. However, if the impurity mass is large enough, a higher-velocity kink will be reflected while a lower-velocity kink will pass. We explain this effect analytically and show that the impurity mode plays an important role in the scattering. In all the cases considered we find good agreements between the collective-coordinate analysis and the direct numerical simulations.
137 citations
TL;DR: It is demonstrated numerically that the kink may be reflected by an attractive impurity when its velocity lies in some windows, and this effect is due to a resonant energy exchange in the kinks translational mode, its internal mode, and the impurity mode.
Abstract: We study kink-impurity interactions in the ${\mathrm{\ensuremath{\varphi}}}^{4}$ model, extending our previous results [Zhang Fei, Y. Kivshar, and L. V\'azquez, Phys. Rev. A 45, 6019 (1992)] to the case where the kink has an internal degree of freedom which may be excited due to scattering. We demonstrate numerically that the kink may be reflected by an attractive impurity when its velocity lies in some ``windows,'' and this effect is due to a resonant energy exchange between the kink translational mode, its internal mode, and the impurity mode. We observe additional features in the resonant interactions, e.g., quasiresonances at some intermediate velocities and ``three-bounce'' resonances. We also develop an analytical approach taking into account three dynamical variables and show that such a collective-coordinate model may explain qualitatively the resonance structures observed in numerical simulations.
103 citations
TL;DR: In this paper, the authors review recent numerical and analytical results related to the coexistence of nonlinear wave propagation and disorder effects, mostly for soliton bearing systems, and demonstrate that nonlinear transmission strongly depends on the soliton type: results are different for dynamical, topological, and envelope solitons.
102 citations
TL;DR: In the limit when the gap disappears, the gap solitons do not exist but instead there exist localized structures of a distinct type created by the nonlinearity-induced symmetry breaking between two equivalent eigenmodes of the lattice, the so-called self-supporting gapsolitons.
Abstract: We consider a nonlinear diatomic lattice of the Klein-Gordon type composed of particles with two different masses. The linear spectrum of this model exhibits a gap, which is proportional to the mass difference in addition to the natural gap stipulated by a nonlinear substrate potential. We analyze the coupled nonlinear excitations of such a diatomic chain which have a similar origin as the well-known gap solitons appearing in nonlinear (e.g., optical) systems with a spatial periodicity. We also describe dark-profile localized structures with a frequency lying below the gap. In the limit when the gap disappears, i.e., for the case of a monoatomic chain, the gap solitons do not exist but instead there exist localized structures of a distinct type created by the nonlinearity-induced symmetry breaking between two equivalent eigenmodes of the lattice, the so-called self-supporting gap solitons.
61 citations
TL;DR: In the limit in which the integrable model approximation is valid, numerical simulations show rather stable bound states of bright and dark pulses as well as their almost elastic collision.
Abstract: The vector optical solitons composed of bright and dark pulses are analyzed. It is shown that in the small-amplitude limit a bound state of these solitons is described by the generalized Zakharov system, which supports coupled soliton solutions, and under special conditions it reduces to an integrable model. In the limit in which the integrable model approximation is valid, numerical simulations show rather stable bound states of bright and dark pulses as well as their almost elastic collision.
52 citations
TL;DR: In this paper, a collective coordinate approach is applied to analyze the effect of an rf signal on the radiation emitted from a long Josephson junction, which shows a variety of interesting nonlinear phenomena including chaos and hysteresis.
17 citations
TL;DR: A spatially periodic perturbation can lead to a breakup of large-amplitude sine-Gordon breathers into kink and antikink solutions, each oscillating around a minimum of the perturbing potential.
Abstract: A spatially periodic perturbation can lead to a breakup of large-amplitude sine-Gordon breathers into kink and antikink solutions, each oscillating around a minimum of the perturbing potential. This behavior can be understood by studying the effective potential experienced by the breather (bound kink-antikink) or the (free) kink-antikink solution as long as kink and antikink are sufficiently far apart. The resulting kinks and antikinks move independently and nearly radiationlessly in the presence of the perturbation and can travel arbitrarily far for sufficiently large initial kinetic energy. Upon interacting with each other they are strongly affected by the perturbation, lose energy by radiating, and can end in a bound state having the character of a distorted breather.
15 citations
TL;DR: The existence of a new class of localized structures in nonlinear lattices is proved analytically and it is pointed out that such excitations have been recently observed experimentally in the form of the so-called noncutoff kinks.
Abstract: The existence of a new class of localized structures in nonlinear lattices is proved analytically and its is pointed out that such excitations have been recently observed experimentally in the form of the so-called noncutoff kinks. These localized structures appear to be due to nonlinearity-induced breaking of symmetry between two equivalent eigenmodes of the lattice, and they probalby exist in a large variety of nonlinear discrete systems
14 citations
TL;DR: An analytical approach based on the method of averaging in fast oscillations predicts that such a parametric force may support propagation of {pi} kinks, which are unstable in the standard sine-Gordon model.
Abstract: We consider the sine-Gordon chain driven by a high-frequency parametric force in the presence of loss. Using an analytical approach based on the method of averaging in fast oscillations, we predict that such a parametric force may support propagation of {pi} kinks, which are unstable in the standard sine-Gordon model. The steady-state velocity of the {pi} kinks is calculated, and the analytical results are in good agreement with direct numerical simulations.
13 citations
TL;DR: There is a range of driving parameters such that kinks cannot exist in the model with loss, which may be understood with the help of an averaged external potential energy of the system, which has no double-well structure in this region.
Abstract: We consider the parametrically driven discrete ${\mathrm{\ensuremath{\varphi}}}^{4}$ model with loss. Using an anaytical approach and direct numerical simulations, which turn out to be in excellent agreement, we demonstrate that there is a range of driving parameters such that kinks cannot exist in the system. This effect may be understood with the help of an averaged external potential energy of the system, which has no double-well structure in this region.
TL;DR: A general method to compute dynamical variable statistics which can be generalized to a number of soliton-bearing systems, and is applied to the sine-Gordon equation as an example.
Abstract: Using a collective-coordinate approach, we study kink propogation along nonlinear systems with local, randomly distributed inhomogeneities. We develop a general method to compute dynamical variable statistics which can be generalized to a number of soliton-bearing systems, and we apply it to the sine-Gordon equation as an example
TL;DR: In this article, it was demonstrated that a sine-Gordon chain may support localized kink solitons, connecting two inverted ground states, if the system is driven by a large-amplitude ac force.
TL;DR: In this paper, the authors consider a nonlinear lattice of the Klein-Gordon type analysing envelope solitons created on a standing carrier wave and show that nonlinear waves of such a kind are described by a system of two coupled nonlinear Schrodinger equations.
TL;DR: In this article, the scattering of nonlinear wavepackets in the form of envelope solitons by a one-dimensional disordered system is studied, and it is shown that strong nonlinearity allows undistorted propagation of these wave-packets.
Abstract: We study the scattering of nonlinear wavepackets in the form of envelope solitons by a one-dimensional disordered system. We briefly review the features of the scattering for linear waves and obtain some results for linear wavepackets to demonstrate their common exponential decay of the transmission coefficient, characterized by a localization length. We consider the same process for envelope solitons, and we show in the framework of the simplest model, that, above a certain threshold, strong nonlinearity allows undistorted propagation of these wavepackets. We describe how this behaviour can be obtained, for the nonlinear Schrodinger equation, by means of a simple independent scattering approach, using results of soliton perturbation theory to compute one-impurity reflection coefficients in the Born approximation. We derive equations to describe the transmission of the soliton parameters and analyse them in full detail. The main result of our study is the conclusion that a strong nonlinearity sti...