Showing papers by "Yuri S. Kivshar published in 1998"
TL;DR: A detailed overview of the physics and applications of optical dark solitons can be found in this article, where the authors discuss the instability-induced dynamics of dark-solitons in the models of generalized (i.e., non-Kerr) optical nonlinearities.
1,076 citations
TL;DR: An overview of the dynamics of one of the fundamental models of low-dimensional nonlinear physics, the Frenkel-Kontorova (FK) model, is presented in this article.
515 citations
TL;DR: In this paper, the authors developed an analytical approach for describing the birth of internal modes of solitary waves in nonintegrable nonlinear models, and showed that a small perturbation of a proper sign to an integrable model can create a soliton internal mode bifurcating from the continuous wave spectrum.
Abstract: We develop an analytical approach for describing a birth of internal modes of solitary waves in nonintegrable nonlinear models We show that a small perturbation of a proper sign to an integrable model can create a soliton internal mode bifurcating from the continuous wave spectrum The theory is applied to the double sine-Gordon and discrete nonlinear Schrodinger equations, and an excellent agreement with numerical data is demonstrated [S0031-9007(98)06329-7]
149 citations
TL;DR: In this paper, the authors extend the concept of internal mode to envelope solitons and show that this mode is responsible for long-lived, weakly damped periodic oscillations of the soliton amplitude observed in numerical simulations.
108 citations
TL;DR: In this article, the drift of an optical vortex soliton created on a slowly diffracting, finite-extend background field is analyzed in the framework of the generalized nonlinear Schrodinger equation.
96 citations
TL;DR: In this article, the existence and stability regimes of bright 211-dimensional spatial solitary waves in media with quadratic and focusing cubic nonlinearities were determined and a necessary criterion for linear stability of these solitons was derived.
Abstract: We determine the existence and stability regimes of bright 211-dimensional spatial solitary waves in media with quadratic ~or x ! and focusing cubic nonlinearities. We derive a necessary criterion for linear stability of these solitons, and use it to show that the quadratic nonlinearity enables stable solitons to exist when the cubic nonlinearity is sufficiently weak. We discuss why the Vakhitov-Kolokolov criterion for stability in x (2) systems is only a necessary criterion, and show an example where it fails. We further derive and study a simple adiabatical model for the soliton dynamics close to the instability threshold. Finally, we study the interesting dynamics of the solitons in the unstable regime, where we demonstrate the existence of two different limits described by nonlinear Schrodinger equations. @S1063-651X~98!15409-0#
52 citations
TL;DR: This work analytically studies the influence of this induced cubic nonlinearity on the amplitude and phase modulation of the fundamental wave and predicts efficient all-optical switching.
Abstract: Recently it was shown that in quasi-phase-matched quadratic media the average intensities are subject to an induced Kerr effect. We analytically study the influence of this induced cubic nonlinearity on the amplitude and phase modulation of the fundamental wave and predict efficient all-optical switching.
39 citations
TL;DR: The structure and stability of different types of multicolor optical spatial solitary waves created by interaction of light at a central frequency with two sideband waves both through cross-phase modulation and parametric four-wave mixing is presented in this paper.
Abstract: The structure and stability of different types of multicolor optical spatial solitary waves created by interaction of light at a central frequency with two sideband waves both through cross-phase modulation and parametric four-wave mixing is presented. It is shown that a novel type of three-color spatial soliton appears above a power threshold when parametric coupling generates an instability of two-frequency solitary waves.
37 citations
TL;DR: A nonlinear theory of soliton-induced waveguides that describes a finite-amplitude probe beam guided by a spatial dark soliton in a saturable nonlinear medium is developed and it is shown that, in sharp contrast with scalar dark solitons, the dark-soliton waveguide can attract each other and even form stationary bound states.
Abstract: We develop a nonlinear theory of soliton-induced waveguides that describe a finite-amplitude probe beam guided by a spatial dark soliton in a saturable nonlinear medium. We suggest an effective way to control the interaction of these soliton-induced waveguides and also show that, in sharp contrast with scalar dark solitons, the dark-soliton waveguides can attract each other and even form stationary bound states.
33 citations
TL;DR: In this article, the (2+1)-dimensional generalized nonlinear Schrodinger equation was used to analyze optical vortex solitons in a defocusing saturable medium with varying saturation parameter.
Abstract: Optical vortex solitons in a defocusing saturable medium are analyzed in the framework of the (2+1)-dimensional generalized nonlinear Schrodinger equation. Stationary, radially symmetric localized solutions with nonvanishing asymptotics and a phase singularity (vortex solitons) are found numerically for the varying saturation parameter. Relaxation of some localized initial profiles (e.g., vortex-type structures of an elliptic shape) to a vortex soliton is investigated numerically and then compared with the experimentally measured propagation of the vortex solitons created by a laser beam passed through a rubidium vapor, known as a nonlinear medium with strong saturation of the nonlinear refractive index. Reasonably good agreement is found, supporting the validity of the phenomenological model of the saturable nonlinear medium.
32 citations
TL;DR: In this article, the effect of phase-matched third-harmonic generation on the existence and stability of (1+1)-dimensional bright and dark spatial solitary waves in optical media with a cubic (or Kerr) nonlinear response was analyzed.
Abstract: We analyze the effect of phase-matched third-harmonic generation on the existence and stability of (1+1)-dimensional bright and dark spatial solitary waves in optical media with a cubic (or Kerr) nonlinear response. We demonstrate that parametric coupling of the fundamental beam with the third harmonic leads to the existence of two-color solitary waves resembling those in a χ(2) medium and that it can modify drastically the properties of solitary waves due to effective non-Kerr nonlinearities. In particular, we find a power threshold for the existence of two-frequency parametric bright solitons and also reveal the soliton multistability in a Kerr medium that becomes possible owing to a higher-order nonlinear phase shift caused by cascaded third-order processes. We also analyze dark solitary waves and their stabilities. We show that, in a certain parameter domain, parametric χ(3) dark solitons may become unstable owing to the modulational instability of the supporting background or to other instability mechanisms caused by the parametric coupling between the harmonics.
TL;DR: In this article, the existence of bound states of intrinsic localized excitations in nonlinear lattices was predicted for a discrete chain with linear and nonlinear cubic interparticle interaction.
Abstract: In the framework of the continuum approximation, localized modes in nonlinear lattices ~''intrinsic localized modes'' or ''discrete breathers'' ! are described by the nonlinear Schrodinger ~NLS! equation. We go beyond this approximation and analyze what kind of qualitatively new effects can be introduced by discreteness. Taking into account the higher-order linear and nonlinear dispersion terms in the NLS equation derived from a lattice model, we predict the existence of bound states of intrinsic localized excitations. These bound states of nonlinear localized modes are also found numerically for a discrete chain with linear and nonlinear cubic interparticle interaction. @S0163-1829~98!05133-9#
TL;DR: It is demonstrated that a weak defocusing Kerr effect in an optical medium with predominantly quadratic [or chi((2))] nonlinear response can eliminate the parametric modulational instability of plane waves, leading to the existence of stable two-wave dark and vortex spatial solitons.
Abstract: We demonstrate that a weak defocusing Kerr effect in an optical medium with predominantly quadratic [or chi((2))] nonlinear response can eliminate the parametric modulational instability of plane waves, leading to the existence of stable two-wave dark and vortex spatial solitons.
TL;DR: In this paper, the structure and stability of nonlinear surface modes in one-dimensional monoatomic and diatomic lattices were investigated and it was shown analytically and numerically that nonlinearity can support a stable surface mode whose maximum amplitude is shifted from the surface.
TL;DR: In this article, a simple all-optical switch based on a bent nonlinear planar waveguide is proposed, which is shown to have effective and controllable switching characteristics, and avoids problems associated with the phenomenon of multisoliton emission.
TL;DR: In this paper, the structure and stability of nonlinear surface modes in a simple one-dimensional lattice model of an adsorbed layer were analyzed, and it was shown that two of these modes are stable while the other one is unstable, and numerically the switching between the unstable and stable surface modes.
TL;DR: In this article, the spin dynamics of a domain wall is studied in an infinite ferromagnetic chain with an easy-axis anisotropy as well as in a chain of finite size.
Abstract: The spin dynamics of a domain wall is studied in an infinite ferromagnetic chain with an easy-axis anisotropy as well as in a chain of finite size. The dependence of the intrinsic mode frequency of the domain wall on the exchange interaction is studied for all admissible values of the latter. It is shown that this dependence is considerably modified in the region of transition of the domain wall from collinear structure to canted form.