arXiv subjects

Dumitru Mihalache

Publications and source records attributed to Dumitru Mihalache.

At least 55 records · Page 3Linked to original sources

arXiv2017

Smooth positon solutions of the focusing modified Korteweg-de Vries equation

The $n$-fold Darboux transformation $T_{n}$ of the focusing real mo\-di\-fied Kor\-te\-weg-de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the $n$-soliton solutions of the mKdV equation are also expressed by determinants whose elements consist of the eigenvalues $λ_{j}$ and the corresponding eigenfunctions of the associated Lax equation. The nonsingular $n$-positon solutions of the focusing mKdV equation are obtained in the special limit $λ_{j}\rightarrowλ_{1}$, from the corresponding $n$-soliton solutions and by using the associated higher-order Taylor expansion. Furthermore, the decomposition method of the $n$-positon solution into $n$ single-soliton solutions, the trajectories, and the corresponding "phase shifts" of the multi-positons are also investigated.

nlin.SI↗

arXiv2017

Construction of rational solutions of the real modified Korteweg-de Vries equation from its periodic solutions

In this paper, we consider the real modified Korteweg-de Vries (mKdV) equation and construct a special kind of breather solution, which can be obtained by taking the limit $λ_{j}$ $\rightarrow$ $λ_{1}$ of the Lax pair eigenvalues used in the $n$-fold Darboux transformation that generates the order-$n$ periodic solution from a constant seed solution. Further, this special kind of breather solution of order $n$ can be used to generate the order-$n$ rational solution by taking the limit $λ_{1}$ $\rightarrow$ $λ_{0}$, where $λ_{0}$ is a special eigenvalue associated to the eigenfunction $ϕ$ of the Lax pair of the mKdV equation. This eigenvalue $λ_0$, for which $ϕ(λ_0)=0$, corresponds to the limit of infinite period of the periodic solution. %This second limit of double eigenvalue degeneration might be realized approximately in optical fibers, in which an injected %initial ideal pulse is created by a comb system and a programmable optical filter according to the profile of the analytical %form of the b-positon at a certain spatial position $x_{0}$. Therefore, we suggest a new way to observe the higher-order %rational solutions in optical fibers, namely, to measure the wave patterns at the central region of the higher order b-positon %generated by ideal initial pulses when the eigenvalue $λ_{1}$ is approaching $λ_{0}$. Our analytical and numerical results show the effective mechanism of generation of higher-order rational solutions of the mKdV equation from the double eigenvalue degeneration process of multi-periodic solutions.

nlin.SI↗

arXiv2017

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrodinger equations with position-dependent effective masses

Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized $\mathcal{PT}$-symmetric Scarf-II potentials. The broken linear PT symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than PT-symmetric ones, but feature similar properties. Our results may suggest new experiments for PT-symmetric nonlinear waves in nonlinear nonuniform optical media.

nlin.PS↗

arXiv2016

Collisions of three-dimensional bipolar optical solitons in an array of carbon nanotubes

We study interactions of extremely short three-dimensional bipolar electromagnetic pulses propagating towards each other in an array of semiconductor carbon nanotubes, along any direction perpendicular to their axes. The analysis provides a full account of the effects of the nonuniformity of the pulses' fields along the axes. The evolution of the electromagnetic field and charge density in the sample is derived from the Maxwell's equations and the continuity equation, respectively. In particular, we focus on indirect interaction of the pulses via the action of their fields on the electronic subsystem of the nanotube array. Changes in the shape of pulses in the course of their propagation and interaction are analyzed by calculating and visualizing the distribution of the electric field in the system. The numerical analysis reveals a possibility of stable post-collision propagation of pulses over distances much greater than their sizes.

physics.optics↗

arXiv2016

Commentary (invited update) to article "Spatiotemporal optical solitons", by B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclass. Opt. 7, R53-R72 (2005)

This is an invited short update of the topic covered by the review article, which aims to briefly survey progress made in theoretical and experimental studies of multidimensional solitons since the publication of the review. The Commentary was invited as an addition to the original review article that will be reprinted in an e-book celebrating the 50th anniversary of Journal of Physics B (incorporating Journal of Optics B: Quantum and Semiclassical Optics).

physics.optics↗

arXiv2014

Breather-like solitons extracted from the Peregrine rogue wave

Based on the Peregrine solution (PS) of the nonlinear Schrödinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breather-like solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realistic values of coefficients accounting for the anomalous dispersion, Kerr nonlinearity, and higher-order effects. The results demonstrate that the breathing solitons stably propagate in the fibers. Their robustness against small random perturbations applied to the initial background is demonstrated too.

physics.optics↗

arXiv2014

Building patterns by traveling vortices and dipoles in periodic dissipative media

We analyze pattern-formation scenarios in the two-dimensional (2D) complex Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity and a cellular potential. The equation models laser cavities with built-in gratings, which are used to stabilize 2D patterns. The pattern-building process is initiated by kicking a localized compound mode, in the form of a dipole, quadrupole, or vortex which is composed of four local peaks. The hopping motion of the kicked mode through the cellular structure leads to the generation of various extended patterns pinned by the structure. In the ring-shaped system, the persisting freely moving dipole hits the stationary pattern from the opposite side, giving rise to several dynamical regimes, with the pinned multi-soliton chain playing the role of the Newton's cradle (NC).

nlin.PS↗

arXiv2014

Localized modes in dissipative lattice media: An overview

We overview recent theoretical studies of the dynamics of one- and two-dimensional spatial dissipative solitons in models based on the complex Ginzburg-Landau equations with the cubic-quintic combination of loss and gain terms, which include imaginary, real, or complex spatially periodic potentials. The imaginary potential represents periodic modulation of the local loss and gain. It is shown that the effective gradient force, induced by the inhomogeneous loss distribution, gives rise to three generic propagation scenarios for one-dimensional (1D) dissipative solitons: transverse drift, persistent swing motion, and damped oscillations. When the lattice-average loss/gain value is zero, and the real potential has spatial parity opposite to that of the imaginary component, the respective complex potential is a realization of the parity-time symmetry. Under the action of lattice potentials of the latter type, 1D solitons feature unique motion regimes in the form of transverse drift and persistent swing. In the 2D geometry, three types of axisymmetric radial lattices are considered, viz., ones based solely on the refractive-index modulation, or solely on the linear-loss modulation, or on a combination of both. The rotary motion of solitons in such axisymmetric potentials can be effectively controlled by varying the strength of the initial tangential kick.

physics.optics↗

arXiv2013

Control of high power pulse extracted from the maximally compressed pulse in a nonlinear optical fiber

We address the possibility to control high power pulses extracted from the maximally compressed pulse in a nonlinear optical fiber by adjusting the initial excitation parameters. The numerical results show that the power, location and splitting order number of the maximally compressed pulse and the transmission features of high power pulses extracted from the maximally compressed pulse can be manipulated through adjusting the modulation amplitude, width, and phase of the initial Gaussian-type perturbation pulse on a continuous wave background.

physics.optics↗

arXiv2013

High power pulses extracted from the Peregrine rogue wave

We address the various initial excitations of the Peregrine rogue wave and establish a robust transmission scheme of high power pulses extracted from the Peregrine rogue wave in a standard telecommunications fiber. The results show that the Peregrine rogue wave can be excited by using a weak pulse atop a continuous wave background and that the high power pulses extracted from the Peregrine rogue wave exhibit the typical characteristics of breathing solitons. The influence of higher-order effects, such as the third-order dispersion, the self-steepening and the Raman effect, on the propagation of the pulse extracted from the peak position and the interaction between neighboring high power pulses induced by initial perturbations are also investigated.

physics.optics↗

arXiv2012

Pattern formation by kicked solitons in the two-dimensionnal Ginzburg-Landau medium with a transverse grating

We consider the kick-induced mobility of two-dimensional (2D) fundamental dissipative solitons in models of lasing media based on the 2D complex Ginzburg-Landau (CGL) equation including a spatially periodic potential (transverse grating). The depinning threshold is identified by means of systematic simulations, and described by means of an analytical approximation, depending on the orientation of the kick. Various pattern-formation scenarios are found above the threshold. Most typically, the soliton, hopping between potential cells, leaves arrayed patterns of different sizes in its wake. In the laser cavity, this effect may be used as a mechanism for selective pattern formation controlled by the tilt of the seed beam. Freely moving solitons feature two distinct values of the established velocity. Elastic and inelastic collisions between free solitons and pinned arrayed patterns are studied too.

nlin.PS↗

arXiv2012

Generations of polygonal soliton clusters and fundamental solitons by radially-azimuthally phase-modulated necklace-ring beams in dissipative systems

We demonstrate that, in a two-dimensional dissipative medium described by the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) equation with the viscous (spectral-filtering) term, necklace rings carrying a mixed radial-azimuthal phase modulation can evolve into polygonal or quasi-polygonal stable soliton clusters, and into stable fundamental solitons. The outcome of the evolution is controlled by the depth and azimuthal anharmonicity of the phase-modulation profile, or by the radius and number of "beads" in the initial necklace ring. Threshold characteristics of the evolution of the patterns are identified and explained. Parameter regions for the formation of the stable polygonal and quasi-polygonal soliton clusters, and of stable fundamental solitons, are identified. The model with the CQ terms replaced by the full saturable nonlinearity produces essentially the same set of the basic dynamical scenarios; hence this set is a universal one for the CGL models.

physics.optics↗

arXiv2012

Stable surface solitons in truncated complex potentials

We show that surface solitons in the one-dimensional nonlinear Schrödinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interval and they exist in focusing and defocusing media. The domains of stability of surface solitons shrink with increase of the amplitude of imaginary part of complex potential.

physics.optics↗

arXiv2011

Ultrashort spatiotemporal optical solitons in quadratic nonlinear media: Generation of line and lump solitons from few-cycle input pulses

By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of both stable line solitons (in the case of a quadratic medium with normal dispersion) and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of the perturbed unstable line soliton into stable lumps for a quadratic nonlinear medium with anomalous dispersion is also given.

physics.optics↗

arXiv2011

Collapse of ultrashort spatiotemporal pulses described by the cubic generalized Kadomtsev-Petviashvili equation

By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the transverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced.

physics.optics↗

arXiv2011

Ultrashort light bullets described by the two-dimensional sine-Gordon equation

By using a reductive perturbation technique applied to a two-level model, this study puts forward a generic two-dimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly varying envelope approximation. Direct numerical simulations show that, in contrast to the long-wave approximation, no collapse occurs, and that robust (2+1)-dimensional ultrashort light bullets may form from adequately chosen few-cycle input spatiotemporal wave forms. In contrast to the case of quadratic nonlinearity, the light bullets oscillate in both space and time and are therefore not steady-state lumps.

physics.optics↗

arXiv2010

Exact exact solutions of the Gross-Pitaevskii equation for stable vortex modes

We construct exact solutions of the Gross-Pitaevskii equation for solitary vortices, and approximate ones for fundamental solitons, in 2D models of Bose-Einstein condensates with a spatially modulated nonlinearity of either sign and a harmonic trapping potential. The number of vortex-soliton (VS) modes is determined by the discrete energy spectrum of a related linear Schrödinger equation. The VS families in the system with the attractive and repulsive nonlinearity are mutually complementary. \emph{% Stable} VSs with vorticity $S\geq 2$ and those corresponding to higher-order radial states are reported for the first time, in the case of the attraction and repulsion, respectively.

cond-mat.quant-gas↗

arXiv2010

Subwavelength Plasmonic Lattice Solitons in Arrays of Metallic Nanowires

We predict theoretically that stable subwavelength plasmonic lattice solitons (PLSs) are formed in arrays of metallic nanowires embedded in a nonlinear medium. The tight confinement of the guiding modes of the metallic nanowires, combined with the strong nonlinearity induced by the enhanced field at the metal surface, provide the main physical mechanisms for balancing the wave diffraction and the formation of PLSs. As the conditions required for the formation of PLSs are satisfied in a variety of plasmonic systems, we expect these nonlinear modes to have important applications to subwavelength nanophotonics. In particular, we show that the subwavelength PLSs can be used to optically manipulate with nanometer accuracy the power flow in ultracompact photonic systems.

physics.optics↗