Soliton Phenomena Research Articles

A Hamiltonian model and soliton phenomenon for a two- mode KdV equation

A Hamiltonian model and soliton phenomenon for a two- mode KdV equation

Hamiltonian formulation of the Klein–Gordon–Maxwell equations

The nonlinear Klein-Gordon-Maxwell equations (NKGM) provide models for the interaction between the electromagnetic field and matter. The relevance of NKGM relies on the fact that they are the "simplest" gauge theory which is invariant under the group of Poincaré. These equations present the interesting phenomenon of solitons. In this paper, we show that NKGM present an Hamiltonian structure and hence they can be written as equations of the first order in t . This fact is not trivial since the Lagrangian does not depend on \partial_{t}\varphi (see sec. 3.3) and a suitable analysis of its structure is necessary. In the last section, we recall a recent result which states the existence of solitons by using the particular structure of the Hamiltonian.

Domain wall arrays, fronts, and bright and dark solitons in a generalized derivative nonlinear Schrödinger equation

We obtain some exact solutions of a generalized derivative nonlinear Schrödinger equation, including domain wall arrays (periodic solutions in terms of elliptic functions), fronts, and bright and dark solitons. In certain parameter domains, fundamental bright and dark solitons are chiral, and the propagation direction is determined by the sign of the self-steepening parameter. Moreover, we also find the chirping reversal phenomena of fronts, and bright and dark solitons, and discuss two different ways to produce the chirping reversal.

Chirped Domain Wall Arrays and Solitary Waves in a Generalized Nonlinear Schrödinger Equation

We study a generalized nonlinear Schrödinger equation, and obtain some exact solutions, including domain wall arrays (periodic solutions in terms of elliptic functions), fronts, bright and dark solitons. In certain parameter domains, fundamental bright and dark solitons show directionality and hence are chiral, and the propagation direction is determined by the sign of the self-steepening parameter. Moreover, the chirping reversal phenomena of bright and dark solitons are found.

Soliton Resonances of the Nonisospectral Modified Kadomtsev-Petviashvili Equation

Many equations possess soliton resonances phenomenon, this paper studies the soliton resonances of the nonisospectral modified Kadomtsev-Petviashvili (mKP) equation by asymptotic analysis.

Single-Cycle Gap Soliton in a Subwavelength Structure

We demonstrate that a single subcycle optical pulse can be generated when a pulse with a few optical cycles penetrates through resonant two-level dense media with a subwavelength structure. The single-cycle gap soliton phenomenon in the full Maxwell-Bloch equations without the frame of the slowly varying envelope and rotating wave approximations is observed. Our study shows that the subwavelength structure can be used to suppress the frequency shift caused by intrapulse four-wave mixing in continuous media and supports the formation of single-cycle gap solitons even in the case when the structure period breaks the Bragg condition. This suggests a way toward shortening high-intensity laser fields to few- and even single-cycle pulse durations.

Study of electrical soliton as transmission pulse for UWB communication

This paper introduced soliton phenomena in nonlinear transmission line,analyzed the principle of electrical soliton and electrical soliton oscillator,and also gave a simulation experiment under the restrictions of bandwidth and emission power permitted by Federal Communications Commission(FCC).The simulation results show that the electrical soliton signal can be used as transmission pulse for UWB.

Painlevé-integrability of a(2+1)-dimensional reaction-diffusion equation: Exact solutions and their interactions

We investigate the singularity structure analysis of a (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion (NLERD) equation by means of the Painlevé (P) test. Following the Weiss et al.'s formalism [J. Math. Phys. 24, 522 (1983)], we prove the arbitrariness of the expansion coefficients of the observables. Thus, without the use of the Kruskal's simplification, we obtain a Bäcklund transformation of the coupled NLERD equation via a consistent truncation procedure stemming from the Weiss 's methodology [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984)]. In the wake of such results, we unveil a typical spectrum of localized and periodic coherent patterns. We also investigate the scattering properties of such structures and we unearth two peculiar soliton phenomena, namely, the fusion and the fission.

Multistability evolution and hysteresis phenomena of dissipative solitons in a passively mode-locked fiber laser with large normal cavity dispersion

We report on the experimental observations of multiple dissipative solitons in a passively mode-locked fiber laser with large normal cavity dispersion. The dynamic evolution of solitons as a function of the pump power is demonstrated, alternately evolving on the stable and unstable states. The proposed laser produces the multiple solitons of up to ten for the pump power of about 406 mW. Multistability and hysteresis phenomena observed in this report are qualitatively distinct from those observed in the large net-anomalous-dispersion conventional-soliton fiber lasers. The experimental results suggest that the accumulation of excessive pulse chirps together with the nonlinear polarization effect play key roles in the multistability operation of dissipative solitons.

Soliton solution and interaction property for a coupled modified Korteweg–de Vries (mKdV) system

Hirota's bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg–de Vries (mKdV) system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this (1+1)-dimensional integrable coupled model.

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.

Supercontinuum generation through cascaded four-wave mixing in photonic-crystal fibers: When picoseconds do it better

By numerically solving the generalized nonlinear Schrödinger equation, we provide a comparative analysis of spectral and temporal transformations of pico and femtosecond laser pulses in a guided mode with a generic dispersion profile typical of a photonic-crystal fiber. We demonstrate that with an appropriate choice of the input laser pulse parameters, picosecond pulses are efficiently transformed into a supercontinuum emission through a cascade of phase-matched four-wave mixing (FWM) processes. For femtosecond pulses, soliton frequency-shifting phenomena tend to arrest such FWM cascades. In this regime, picosecond pulses can provide much higher efficiencies of supercontinuum generation, as well as much broader and much smoother spectra of output radiation compared to femtosecond pulses with the same peak power.

The Fission, Fusion and Annihilation of Solitons of the (2+1)-Dimensional Broer-Kaup-Kupershmidt System

By means of an improved mapping approach, a series of excitations of the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) system is derived. Based on the derived solitary wave excitation, some specific fission, fusion and annihilation phenomena of solitons are also obtained. - PACS numbers: 05.45.Yv, 03.65.Ge.

Soliton percolation in random optical lattices

We introduce soliton percolation phenomena in the nonlinear transport of light packets in suitable optical lattices with random properties. Specifically, we address lattices with a gradient of the refractive index in the transverse plane, featuring stochastic phase or amplitude fluctuations, and we discover the existence of a disorder-induced transition between soliton insulator and soliton-conductor regimes. The soliton current is found to reach its maximal value at intermediate disorder levels and to drastically decrease in both, almost regular and strongly disordered lattices.

Pulse compression and multimegawatt optical solitons in hollow photonic-crystal fibers

Solitonic phenomena in hollow photonic-crystal fibers are shown to offer new solutions for the control, transmission, and spectral-temporal transformation of ultrashort high-power laser pulses. With the initial parameters of laser radiation accurately matched with fiber dispersion and nonlinearity, submicrojoule laser pulses are shown to exhibit a self-compression and soliton dynamics in the regime of anomalous dispersion. Regimes of solitonic pulse evolution giving rise to few-cycle field waveforms are demonstrated. Based on simple arguments of soliton theory, we derive semiempirical relations providing interesting insights into the minimum pulse width of the laser field in a hollow photonic-crystal fiber as a function of the input laser energy.

A local discontinuous Galerkin method for the Korteweg–de Vries equation with boundary effect

A local discontinuous Galerkin method for solving Korteweg–de Vries (KdV)-type equations with non-homogeneous boundary effect is developed. We provide a criterion for imposing appropriate boundary conditions for general KdV-type equations. The discussion is then focused on the KdV equation posed on the negative half-plane, which arises in the modeling of transition dynamics in the plasma sheath formation [H. Liu, M. Slemrod, KdV dynamics in the plasma-sheath transition, Appl. Math. Lett. 17(4) (2004) 401–410]. The guiding principle for selecting inter-cell fluxes and boundary fluxes is to ensure the L 2 stability and to incorporate given boundary conditions. The local discontinuous Galerkin method thus constructed is shown to be stable and efficient. Numerical examples are given to confirm the theoretical result and the capability of this method for capturing soliton wave phenomena and various boundary wave patterns.

A Kink-Soliton Model of Charge Transport through Microtubular Cytoskeleton

Contemporary trends in science and technology are characterized by integration of biological and technical systems, like in nanotechnology, nanobiology, and quantum medicine. In our case, we were motivated by a necessity to understand charge transport through microtubular cytoskeleton as a constitutive part of acupuncture system. The high frequency component of acupuncture currents, widely exploited in microwave resonance stimulation of acupuncture system in the past decade, implies that explanation of the cytoplasmatic conductivity should be sought in the framework of Frohlich theory. Accordingly, in this paper we critically analyze the problem of the microwave coherent longitudinal electrical oscillations as a theoretical basis for understanding soliton phenomena in microtubules, showing that charged kink-soliton nonlinear microtubular excitations might be a good candidate for charge transport in microtubules.

Soliton self-frequency shift of 6-fs pulses in photonic-crystal fibers

Raman soliton phenomena in photonic crystal fibers are shown to allow efficient tunable frequency shifting of sub-10-fs laser pulses. Soliton self-frequency shift in a photonic-crystal fiber with a core diameter less than 2 μm is used to transform the spectrum of a 6-fs 2-nJ Ti: sapphire-laser pulse, dominated by a 670-nm peak, into a spectrum featuring a well-resolved intense spectral component centered at 1064 nm, which is ideally suited as a seed for Nd: YAG- and ytterbium-based laser devices.

Analytical tools for solitons and periodic waves corresponding to phonons on Lennard-Jones lattices in helical proteins

We study the propagation of solitons along the hydrogen bonds of an alpha helix. Modeling the hydrogen and peptide bonds with Lennard-Jones potentials, we show that the solitons can appear spontaneously and have long lifetimes. Remarkably, even if no explicit solution is known for the Lennard-Jones potential, the solitons can be characterized analytically with a good quantitative agreement using formulas for a Toda potential with parameters fitted to the Lennard-Jones potential. We also discuss and show the robustness of the family of periodic solutions called cnoidal waves, corresponding to phonons. The soliton phenomena described in the simulations of alpha helices may help to explain recent x-ray experiments on long alpha helices in Rhodopsin where a long lifetime of the vibrational modes has been observed.

Spectrally and temporally isolated Raman soliton features in microstructure fibers visualized by cross-correlation frequency-resolved optical gating

We study soliton phenomena accompanying the propagation of femtosecond Cr: forsterite-laser pulses through a microstructure fiber in the regime of efficient anti-Stokes frequency conversion. The dispersion of the fiber is designed in such a way as to minimize the group delay of the 1.25-μm pump and the Stokes pulse within the length of soliton pulse compression in the regime of anomalous dispersion. Spectrally and temporally isolated solitonic features, resulting from soliton self-frequency shift, are detected at the output of such a microstructure fiber by means of cross-correlation frequency-resolved optical gating.