Soliton Systems Research Articles

Stability of solitonic solutions of Super KdV equations under susy breaking conditions

A supersymmetric breaking procedure for N = 1 Super Korteweg-de Vries (SKdV), preserving the positivity of the hamiltonian as well as the existence of solitonic solutions, is implemented. The resulting solitonic system is shown to have nice stability properties.

The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of super Korteweg-de Vries equations

A supersymmetric breaking procedure for N = 1 super Korteweg-de Vries (KdV), using a Clifford algebra, is implemented. Dirac's method for the determination of constraints is used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting solitonic system of coupled KdV type system. It is shown that the Hamiltonian obtained by this procedure is bounded from below and in that sense represents a model which is physically admissible.

Effect of line coding on jitter and initial laser phase on Q value in soliton transmission

In this paper we described how different line coding techniques vary with values of jitter in soliton transmission system. Then the idea of this soliton transmission system is applied for multiuser structure and effects of initial line phase spacing are examined.

132 μm mode-locked bismuth-doped fiber laser operating in anomalous and normal dispersion regimes

We demonstrate a 1.32 μm mode-locked bismuth fiber laser operating in both anomalous and normal dispersion regimes. In anomalous dispersion regime, achieved by using 13 nm/cm linearly chirped fiber Bragg grating, the laser exhibits multiple soliton operation with pulse duration of 2.51 ps. With the net normal cavity dispersion, the single-pulse operation with higher power has been obtained by avoiding the limitations generic to conservative soliton systems.

A possibility for generation of two species of charge carriers along main-chain and side-chains for a π-conjugated polymer

Iodide doping produces charge carriers in π-conjugated polymers. Solitons can be generated in the case of polyacetylene, and polarons in the case of aromatic-type conjugated polymers. We synthesized a conjugated main-chain/side-chain polymer, which consists of polyene in the main-chain and aromatic-type conjugated units in the side-chains. Based on the SSH (Su, Schrieffer, Heeger) theoretical model of solitons in one-dimensional conjugated polymers, we experimentally carried out chemical doping to the main-chain/side-chains conjugated polymer. Generation of the charge carriers was examined by electron spin resonance spectroscopy. This study may lead to realization of a dual doping system of solitons and polarons in π-conjugation expanded to two-dimensional directions in polymers.

Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems

We investigate a peculiar supersymmetry of the pairs of reflectionless quantum mechanical systems described by $n$-soliton potentials of a general form that depends on $n$ scaling and $n$ translation parameters. We show that if all the discrete energy levels of the subsystems are different, the superalgebra, being insensitive to translation parameters, is generated by two supercharges of differential order $2n$, two supercharges of order $2n+1$, and two bosonic integrals of order $2n+1$ composed from Lax integrals of the partners. The exotic supersymmetry undergoes a reduction when $r$ discrete energy levels of one subsystem coincide with any $r$ discrete levels of the partner; the total order of the two independent intertwining generators reduces then to $4n\ensuremath{-}2r+1$, and the nonlinear superalgebraic structure acquires a dependence on $r$ relative translations. For a complete pairwise coincidence of the scaling parameters which control the energies of the bound states and the transmission scattering amplitudes, the emerging isospectrality is detected by a transmutation of one of the Lax integrals into a bosonic central charge. Within the isospectral class, we reveal a special case giving a new family of finite-gap first order Bogoliubov-de Gennes systems related to the Ablowitz-Kaup-Newell-Segur integrable hierarchy.

Dissipative Soliton Excitability Induced by Spatial Inhomogeneities and Drift

We show that excitability is generic in systems displaying dissipative solitons when spatial inhomogeneities and drift are present. Thus, dissipative solitons in systems which do not have oscillatory states, such as the prototypical Swift-Hohenberg equation, display oscillations and type I and II excitability when adding inhomogeneities and drift to the system. This rich dynamical behavior arises from the interplay between the pinning to the inhomogeneity and the pulling of the drift. The scenario presented here provides a general theoretical understanding of oscillatory regimes of dissipative solitons reported in semiconductor microresonators. Our results open also the possibility to observe this phenomenon in a wide variety of physical systems.

Ionization effects in the generation of wake-fields by ultra-high contrast femtosecond laser pulses in argon gas

Difference in mechanisms of wake-field generation and electron self-injection by high contrast femtosecond laser pulses in an initially neutral Argon gas and in pre-ionized plasma without ionization is studied via 2D particle-in-cell simulations including optical ionization of the media. For shorter laser pulses, 40 fs, ionization results only in an increase of the charge of accelerated electrons by factor of ∼3 with qualitatively the same energy distribution. For longer pulses, 80 fs, a more stable wake field structure is observed in the neutral gas with the maximal energy of the accelerated electrons exceeding that in the fixed density plasma. In higher density Argon, an ionizing laser pulse converts itself to a complex system of solitons at a self-induced, critical density ramp.

Bright solitons in defocusing media with spatial modulation of the quintic nonlinearity

It has been recently demonstrated that self-defocusing (SDF) media with cubic nonlinearity, whose local coefficient grows from the center to the periphery fast enough, support stable bright solitons without the use of any linear potential. Our objective is to test the genericity of this mechanism for other nonlinearities, by applying it to one- and two-dimensional (1D and 2D) quintic SDF media. The models may be implemented in optics (in particular, in colloidal suspensions of nanoparticles), and the 1D model may be applied to the description of the Tonks-Girardeau gas of ultracold bosons. In 1D, the nonlinearity-modulation function is taken as g0+sinh2(βx). This model admits a subfamily of exact solutions for fundamental solitons. Generic soliton solutions are constructed in a numerical form and also by means of the Thomas-Fermi and variational approximations (TFA and VA). In particular, a new ansatz for the VA is proposed, in the form of "raised sech," which provides for an essentially better accuracy than the usual Gaussian ansatz. The stability of all the fundamental (nodeless) 1D solitons is established through the computation of the corresponding eigenvalues for small perturbations and also verified by direct simulations. Higher-order 1D solitons with two nodes have a limited stability region, all the modes with more than two nodes being unstable. It is concluded that the recently proposed inverted Vakhitov-Kolokolov stability criterion for fundamental bright solitons in systems with SDF nonlinearities holds here too. Particular exact solutions for 2D solitons are produced as well.

Construction and separability of nonlinear soliton integrable couplings

The paper is motivated by recent works of several authors, initiated by articles of Ma and Zhu [W. X. Ma, Z. N. Zhu, Constructing nonlinear discrete integrable Hamiltonian couplings, Comput. Math. Appl. 60 (2010) 2601] and Ma [W. X. Ma, Nonlinear continuous integrable Hamiltonian couplings, Appl. Math. Comput. 217 (2011) 7238], where new class of soliton systems, being nonlinear integrable couplings, was introduced. Here, we present a general construction of such class of systems and we develop the decoupling procedure, separating them into copies of underlying original equations.

Optimum dispersion map profile for a stable DM soliton system

This paper investigates the optimum dispersion map profile for stable DM soliton formation and propagation. Results of numerical analysis suggest that anomalous–normal–normal–anomalous (A-N-N-A) profile is the most suitable one for a dispersion map with perfect dispersion compensation. DM soliton stability and propagation behavior has been further explored for an undercompensated A-N-N-A profile which increases the distance for stable propagation but requires a positive initial chirp. The stability region has been identified for such DM links in the parametric space of residual dispersion and initial chirp. The study of DM soliton interaction and collision dynamics indicates that a DM soliton formed in such stable parametric space offers improved spectral efficiency as compared to the fundamental solitons.

Wide localized solitons in systems with time- and space-modulated nonlinearities

In this work we apply point canonical transformations to solve some classes of nonautonomous, nonlinear Schrödinger equations, namely, those which possess specific cubic and quintic (time- and space-dependent) nonlinearities. In this way we generalize some procedures recently published which resort to an ansatz to the wave function and recover a time- and space-independent nonlinear equation which can be solved explicitly. The method applied here allows us to find wide localized (in space) soliton solutions to the nonautonomous, nonlinear Schrödinger equation. We also generalize the external potential which traps the system and the terms of the nonlinearities.

Ermakov–Ray–Reid Reductions of Variational Approximations in Nonlinear Optics

Integrable Hamiltonian systems of Ermakov‐Ray‐Reid type are shown to arise out of variational approximation to certain modulated NLS models as well as in spiralling elliptic soliton systems and their generalization in a Bose‐Einstein setting.

The Neumann system for the 4th-order eigenvalue problem and constraint flows of the coupled KdV-type equations

� Societa Italiana di Fisica / Springer-Verlag 2012 Abstract. In this paper, the Neumann system for the 4th-order eigenvalue problem Ly =( ∂ 4 +q∂ 2 + ∂ 2 q + ip∂ +i∂p+r)y = Λy has been given. By means of the Neumann constraint condition, the perfect constraint set Γ and the relations between the potentials {q, p, r} and the eigenvector y are obtained. Then, based on the Euler-Lagrange function and Legendre transformations, a reasonable Jacobi-Ostrogradsky coor- dinate system has been found, which can be equal to the real Hamiltonian canonical coordinate system in R 8N. Using Cao's method and Moser's constraint manifold, the Lax pairs of the evolution equation hierarchy with the 4th-order eigenvalue problems are nonlinearized. So a new finite-dimensional integrable Hamilton system on the constraint submanifold R 8N −4 is generated. Moreover, the solutions of the evo- lution equations for the infinite-dimensional soliton systems are obtained by the involutive flow of the finite-dimensional completely integrable systems.

Optimum amplifier location for wavelength division multiplexed dispersion managed solitons

Using a variational method, we analyze the residual frequency shifts due to cross-channel interactions in wavelength division multiplexed dispersion managed soliton transmission systems. We put forward a simple criterion for the optimal location of the amplifier based on the results of this analysis. This conclusion is explained in terms of the dependence of the propagation properties of a single pulse on the position of the amplifier and the optimality of the criterion is assessed, for some specific parameter values, using a commercial simulation software.

On fractional quantum Hall solitons and Chern–Simons quiver gauge theories

We investigate a class of hierarchical multiple layers of fractional quantum Hall soliton (FQHS) systems from Chern–Simons quivers embedded in M-theory on the cotangent on a two-dimensional complex toric variety V2, which is dual to type IIA superstring on a three-dimensional complex manifold CP1 × V2 fibered over a real line . Based on M-theory/type IIA duality, FQHS systems can be derived from wrapped D4-branes on 2-cycles in CP1 × V2 type IIA geometry. In this realization, the magnetic source can be identified with gauge fields obtained from the decomposition of the R–R 3-form on a generic combination of 2-cycles. Using type IIA D-brane flux data, we compute the filling factors for models relying on CP2 and the zeroth Hirzebruch surface.

Controllable rogue waves in the nonautonomous nonlinear system with a linear potential

Based on the similarity transformation connected the nonautonomous nonlinear Schrodinger equation with the autonomous nonlinear Schrodinger equation, we firstly derive self-similar rogue wave solutions (rational solutions) for the nonautonomous nonlinear system with a linear potential. Then, we investigate the controllable behaviors of one-rogue wave, two-rogue wave and rogue wave triplets in a soliton control system. Our results demonstrate that the propagation behaviors of rogue waves, including postpone, sustainment, recurrence and annihilation, can be manipulated by choosing the relation between the maximum value of the effective propagation distance Z m and the parameter Z 0. Moreover, the excitation time of controllable rogue waves is decided by the parameter T 0.

Controllable behaviours of rogue wave triplets in the nonautonomous nonlinear and dispersive system

A similarity transformation connecting the variable coefficient nonlinear Schrödinger equation with the standard nonlinear Schrödinger equation is constructed. The self-similar rogue wave triplet solutions (rational solutions) are analytically obtained for the nonautonomous nonlinear and dispersive system. The controllable behaviours of rogue wave triplets in two typical soliton management systems are discussed. In the exponential dispersion decreasing fibre, three kinds of rogue wave triplets with controllable behaviours are analysed. In the periodic distributed system, the rogue wave triplets recur periodically in the form of a cluster.

Soliton interactions in some semidiscrete integrable systems

In this paper, soliton interactions in three semidiscrete integrable systems are studied. It will be shown that in some cases the solitary waves of the semidiscrete integrable systems can interact elastically, i.e., the shapes, the amplitudes, and the velocities of waves preserve after undergoing collision. However, soliton interactions in the semidiscrete integrable systems possess different properties from the continuous solitons, for example, the shorter waves can travel faster than the taller ones. We also find that two stable solitary waves can be destroyed after interaction, and the elastic properties of collisions between two solitary waves are sensitively dependent on the choices of some parameters in solution. We therefore conclude that soliton interactions in semidiscrete integrable systems are richer than the ones in continuous soliton systems.

Generation of a New Coupled Ultra-Short Pulse System from a Group Theoretical Viewpoint: the Cartan Ehresman Connection

Based upon the group theoretical jet bundle formalism introduced by Wahlquist and Estabrook for discussing the complete integrability of soliton systems, we investigate the prolongation structure of Wadati—Konno—Ichikawa isospectral evolution equations. As a result, we unearth a new physical coupled system entailing a hidden structural symmetry SL(3, R) arising in the description of ultra-short pulse propagation in optical nonlinear media. As a matter of fact, we depict a graphical representation of one-breather and two-breather ultra-short pulses in motion with a non-zero angular momentum. By extending the previous study to multidimensional symmetry SL(n, R), we unearth a more general class of multicomponent coupled nonlinear ultra-short pulse system with its associated inverse scattering formulation particularly useful in soliton theory.