Biomedical subjects

BA Malomed

Publications and source records attributed to BA Malomed.

At least 19 recordsLinked to original sources

PubMed2000

Nonsteady condensation and evaporation waves

We study the motion of a phase transition (PT) front at a constant temperature between stable and metastable states in fluids with the van der Waals equation of state. We focus on a case of relatively large metastability and low viscosity, when no steadily moving PT front exists. Simulating the one-dimensional hydrodynamic equations, we find that the PT front generates acoustic shocks in forward and backward directions. Through this mechanism, the nonsteady PT front drops its velocity and eventually stops. The shock wave may shuttle between the PT front and the system's edge, rarefaction waves appearing in the shuttle process. If the viscosity is below a certain threshold, a turbulent state sets in.

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PubMed2000

Spatiotemporally localized multidimensional solitons in self-induced transparency media

"Light bullets" are multidimensional solitons which are localized in both space and time. We show that such solitons exist in two- and three-dimensional self-induced transparency media and that they are fully stable. Our approximate analytical calculation, backed and verified by direct numerical simulations, yields the multidimensional generalization of the one-dimensional sine-Gordon soliton.

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PubMed2000

Soliton formation from a pulse passing the zero-dispersion point in a nonlinear Schrodinger equation

We consider in detail the self-trapping of a soliton from a wave pulse that passes from a defocusing region into a focusing one in a spatially inhomogeneous nonlinear waveguide, described by a nonlinear Schrodinger equation in which the dispersion coefficient changes its sign from normal to anomalous. The model has direct applications to dispersion-decreasing nonlinear optical fibers, and to natural waveguides for internal waves in the ocean. It is found that, depending on the (conserved) energy and (nonconserved) "mass" of the initial pulse, four qualitatively different outcomes of the pulse transformation are possible: decay into radiation; self-trapping into a single soliton; formation of a breather; and formation of a pair of counterpropagating solitons. A corresponding chart is drawn on a parametric plane, which demonstrates some unexpected features. In particular, it is found that any kind of soliton(s) (including the breather and counterpropagating pair) eventually decays into pure radiation with an increase of energy, the initial "mass" being kept constant. It is also noteworthy that a virtually direct transition from a single soliton into a pair of symmetric counterpropagating ones seems possible. An explanation for these features is proposed. In two cases when analytical approximations apply, viz., a simple perturbation theory for broad initial pulses and the variational approximation for narrow ones, comparison with direct simulations shows reasonable agreement.

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PubMed2000

Embedded solitons in a three-wave system

We report a rich spectrum of isolated solitons residing inside (embedded into) the continuous radiation spectrum in a simple model of three-wave spatial interaction in a second-harmonic-generating planar optical waveguide equipped with a quasi-one-dimensional Bragg grating. An infinite sequence of fundamental embedded solitons is found, each one differing by the number of internal oscillations. Branches of these zero-walkoff spatial solitons give rise, through bifurcations, to several secondary branches of walking solitons. The structure of the bifurcating branches suggests a multistable configuration of spatial optical solitons, which may find straightforward applications for all-optical switching.

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PubMed2000

Stable solitons of quadratic ginzburg-landau equations

We present a physical model based on coupled Ginzburg-Landau equations that supports stable temporal solitary-wave pulses. The system consists of two parallel-coupled cores, one having a quadratic nonlinearity, the other one being effectively linear. The former core is active, with bandwidth-limited amplification built into it, while the latter core has only losses. Parameters of the model can be easily selected so that the zero background is stable. The model has nongeneric exact analytical solutions in the form of solitary pulses ("dissipative solitons"). Direct numerical simulations, using these exact solutions as initial configurations, show that they are unstable; however, the evolution initiated by the exact unstable solitons ends up with nontrivial stable localized pulses, which are very robust attractors. Direct simulations also demonstrate that the presence of group-velocity mismatch (walkoff) between the two harmonics in the active core makes the pulses move at a constant velocity, but does not destabilize them.

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PubMed2000

Spontaneous symmetry breaking and switching in planar nonlinear optical antiwaveguides

We consider guided light beams in a nonlinear planar structure described by the nonlinear Schrodinger equation with a symmetric potential hill. Such an "antiwaveguide" (AWG) structure induces a transition from symmetric to asymmetric modes via a transcritical pitchfork bifurcation, provided that the beam's power exceeds a certain critical value. It is shown analytically that the asymmetric modes always satisfy the Vakhitov-Kolokolov (necessary) stability criterion; nevertheless, the application of a general Jones' theorem shows that the AWG modes are always unstable. To realize the actual character of the instability, we perform direct numerical simulations, which reveal that a deflecting instability, which drives the asymmetric beam into the cladding without giving rise to fanning or stripping of the beam, sets in after a propagation distance of approximately 16 transverse widths of the AWG's core. The symmetry-breaking bifurcation, in combination with the deflecting instability, may be used to design an all-optical switch. The switching can easily be controlled by means of a symmetry-breaking "hot spot" that acts upon an initial symmetric beam launched with a power exceeding the bifurcation value.

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PubMed2000

Three-dimensional walking spatiotemporal solitons in quadratic media

Two-parameter families of chirped stationary three-dimensional spatiotemporal solitons in dispersive quadratically nonlinear optical media featuring type-I second-harmonic generation are constructed in the presence of temporal walk-off. Basic features of these walking spatiotemporal solitons, including their dynamical stability, are investigated in the general case of unequal group-velocity dispersions at the fundamental and second-harmonic frequencies. In the cases when the solitons are unstable, the growth rate of a dominant perturbation eigenmode is found as a function of the soliton wave number shift. The findings are in full agreement with the stability predictions made on the basis of a marginal linear-stability curve. It is found that the walking three-dimensional spatiotemporal solitons are dynamically stable in most cases; hence in principle they may be experimentally generated in quadratically nonlinear media.

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PubMed2000

Spontaneous pattern formation in driven nonlinear lattices

We demonstrate the spontaneous formation of spatial patterns in a damped, ac-driven cubic Klein-Gordon lattice. These patterns are composed of arrays of intrinsic localized modes characteristic for nonlinear lattices. We analyze the modulation instability leading to this spontaneous pattern formation. Our calculation of the modulational instability is applicable in one- and two-dimensional lattices; however, in the analyses of the emerging patterns we concentrate particularly on the two-dimensional case.

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PubMed2000

Stabilization of dark solitons in the cubic ginzburg-landau equation

The existence and stability of exact continuous-wave and dark-soliton solutions to a system consisting of the cubic complex Ginzburg-Landau (CGL) equation linearly coupled with a linear dissipative equation is studied. We demonstrate the existence of vast regions in the system's parameter space associated with stable dark-soliton solutions, having the form of the Nozaki-Bekki envelope holes, in contrast to the case of the conventional CGL equation, where they are unstable. In the case when the dark soliton is unstable, two different types of instability are identified. The proposed stabilized model may be realized in terms of a dual-core nonlinear optical fiber, with one core active and one passive.

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PubMed2000

Shock wave dynamics in a discrete nonlinear Schrodinger equation with internal losses

Propagation of a shock wave (SW), converting an energy-carrying domain into an empty one, is studied in a discrete version of the normal-dispersion nonlinear Schrodinger equation with viscosity, which may describe, e.g., an array of optical fibers in a weakly lossy medium. It is found that the SW in the discrete model is stable, as well as in its earlier studied continuum counterpart. In a strongly discrete case, the dependence of the SWs velocity upon the amplitude of the energy-carrying background is found to obey a simple linear law, which differs by a value of the proportionality coefficient from a similar law in the continuum model. For the underdamped case, the velocity of the shock wave is found to be vanishing along with the viscosity constant. We argue that the latter feature is universal for long but finite systems, both discrete and continuum. The dependence of the SW's width on the parameters of the system is also discussed.

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PubMed2000

Bragg-grating solitons in a semilinear dual-core system

We investigate the existence and stability of gap solitons in a double-core optical fiber, where one core has the Kerr nonlinearity and the other one is linear, with the Bragg grating (BG) written on the nonlinear core, while the linear one may or may not have a BG. The model considerably extends the previously studied families of BG solitons. For zero-velocity solitons, we find exact solutions in a limiting case when the group-velocity terms are absent in the equation for the linear core. In the general case, solitons are found numerically. Stability borders for the solitons are found in terms of an internal parameter of the soliton family. Depending on the frequency omega, the solitons may remain stable for large values of the group velocity in the linear core. Stable moving solitons are also found. They are produced by interaction of initially separated solitons, which shows a considerable spontaneous symmetry breaking in the case when the solitons attract each other.

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PubMed2000

Azimuthal instability of spinning spatiotemporal solitons

We find one-parameter families of three-dimensional spatiotemporal bright vortex solitons (doughnuts, or spinning light bullets), in dispersive quadratically nonlinear media. We show that they are subject to a strong instability against azimuthal perturbations, similarly to the previously studied (2+1)-dimensional bright spatial vortex solitons. The instability breaks the spinning soliton into several fragments, each being a stable nonspinning light bullet.

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PubMed2000

Crystallization kinetics and self-induced pinning in cellular patterns

Within the framework of the Swift-Hohenberg model it is shown numerically and analytically that the front propagation between cellular and uniform states is determined by periodic nucleation events triggered by the explosive growth of the localized zero-eigenvalue mode of the corresponding linear problem. We derive an evolution equation for this mode using asymptotic analysis, and evaluate the time interval between nucleation events, and hence the front speed. In the presence of noise, we find the velocity exponent of "thermally activated" front propagation (creep) beyond the pinning threshold.

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PubMed2000

Spatiotemporally localized solitons in resonantly absorbing bragg reflectors

We predict the existence of multidimensional solitons that are localized in both space and time ("light bullets") in two- and three-dimensional self-induced-transparency media embedded in a Bragg grating. These fully stable light bullets suggest new possibilities of signal transmission control and self-trapping of light.

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PubMed1996