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Gursey proposed a spinor field equation which is similar to Heisenberg’s nonlinear generalization of Dirac’s equation. This equation is the first nonlinear conformal invariant wave equation. In this paper, we investigate the soliton solutions in Gursey wave equation held in a tilted bichromatic force by constructing their Poincar´e sections in phase space depending on the system parameters. [ABSTRACT FROM AUTHOR]

In the present paper, we study propagation of a soliton at an interface formed between special type of chalcogenide fibre and gallium in three different phases with the help of equivalent particle theory. Critical angle of incidence and critical power required for transmission and reflection of soliton beam have investigated. Here it is found that if the incident angle of the beam or initial velocity of the equivalent particle is insufficient to overcome the maximum increase in potential energy then the particle (light beam) is reflected by the interface and if this incident angle is greater than a critical angle then light beam will be transmitted by the interface. From an equation these critical angles for α-gallium, one of a metastable phase and liquid gallium are calculated and concluded that at large incident angles, the soliton is transmitted through the boundary, whereas at small incidence angles the soliton get reflected on keeping the power of incident beam constant. These results are explained by phase plane trajectories of the effective potential which are experimentally as well as theoretically proved. [ABSTRACT FROM AUTHOR]

The Cubic-Quintic Nonlinear Schrödinger Equation (CQNLSE) is one of the universal mathematical models constituting many interesting problems in physics such as plasma physics, condensed matter physics, Bose-Einstein condensates, nonlinear optics, etc. This paper studies the scattering of the soliton of the CQNLSE on the localized external potential namely Gaussian potential. The approximate analytical method, also known as variational method has been applied in order to derive the equations for soliton parameters evolution during the scattering process. The validity of approximations was tested by direct numerical simulations of CQNLSE with soliton initially located far from potential. It was shown, in case of the potential in the form of Gaussian function, that depending on initial velocity of the soliton, the soliton may be reflected by potential or transmitted through it. The critical values of the velocity separating these two scenarios have been identified. [ABSTRACT FROM AUTHOR]

The free-surface flow generated by multiple bumps at the bottom topography in a rectangular channel was considered, in the framework of the forced Korteweg-de Vries (fKdV) equation. The fKdV equation will be solved numerically using pseudo-spectral method as an analytical solution could not be obtained due to the presence of forcing term and broken symmetry. Various interaction patterns of solitary waves with certain parameter regimes were observed and presented in various graphical forms. Interesting interaction patterns of the collision between uniformly forced solitons will provide us with a better understanding of the hindrance caused by multiple bumps at the uneven bottom topography and it will have a high impact on the water flow in a rectangular channel with uneven bottom topography. [ABSTRACT FROM AUTHOR]

We investigate complexes of localized states in two dynamical systems: (i) directly driven nonlinear Schrödinger equation (NLS) and (ii) double sine-Gordon equation (2SG). Our numerical approach is based on the numerical continuation with respect to the control parameters of the stationary solutions and stability analysis by means of the linearized eigenvalue problem. We show that in the weak damping case the directly driven NLS equation holds stable and unstable multi-soliton complexes. We also show that the second harmonic changes properties and increases the complexity of coexisting static fluxons of 2SG equation. [ABSTRACT FROM AUTHOR]

We study propagation of strain waves in nonlinear hyperelastic media with microstructure. As an illustrative example, a 1D model of a layered composite material is considered. Numerical results are presented and practical relevancy of the above mentioned effects is discussed. [ABSTRACT FROM AUTHOR]

The effect of dust charge fluctuations on the existence and propagation of dust acoustic waves in unmagnified dusty plasma is studied. Dispersion relation for the dust acoustic waves with temporal dust charge fluctuations is calculated based on the reductive perturbation technique. It is shown that when the dust charging frequency is comparable to the dust acoustic wave frequency, the condition give rise to collision less damping of two existing normal modes and one purely damped mode. In the limit when the charging frequency is very much higher than the wave frequency, it is then possible to derive a nonlinear Schrödinger type equation with envelope soliton as solution. [ABSTRACT FROM AUTHOR]

Soliton resonance of integrable hierarchies is one of attractive topics in recent studies. This paper studies resonance property of the nonisospectral(NI-) BKP equation with the help of Hirota bilinear method. [ABSTRACT FROM AUTHOR]

Optical supercontinuum is typically produced by passing short light pulses through a piece of photonic crystal ‘holey’ fiber; by nonlinear interactions the spectrum is dramatically broadened. This has become an established method to provide broadband light as required for various applications. Here we report on a scheme which uses such a fiber in a resonator arrangement so that optical feedback will enhance the effect. This provides additional degrees of freedom for optimization, and it reduces power requirements. [ABSTRACT FROM AUTHOR]

In this paper we present a theorem showing the reason of the connection between Bernoulli numbers and solitons, the solutions of the Korteweg-de Vries equation. The theorem involves Eulerian numbers and Riccati’s differential equation. [ABSTRACT FROM AUTHOR]

When an intense short laser pulse interacts with plasmas, the nonlinear interaction causes various phenomena such as high energy particle generation, strong radiation in the x-ray to THz frequency range. Formation of solitons is one of these interesting topics and has been studied mainly from theoretical aspects. Solitons are formed in an underdense plasma in the process of the laser pulse frequency downshift. They store a portion of the EM wave energy with the polarization inherited from the laser pulse-driver and emit it at the plasma-vacuum interface in the form of low frequency EM bursts. Solitons were observed experimentally by proton-beam imaging and in the visible-near-infrared emissions from the plasma. A low frequency EM radiation emission has also been observed in our experiments. The interpretation invokes the relativistic electromagnetic solitons. We present the results of the polarization-resolved measurements of low frequency radiation from the plasma region irradiated by the intense laser pulse. A dominant component of the observed THz radiation has the same polarization as the driver laser pulse. [ABSTRACT FROM AUTHOR]

Symmetry broken electronic states give rise to topological defects: from extended domain walls—“stripes” as solitonic lattices to microscopic solitons as anomalous quasi-particles and instantons in their dynamics. We shall collect and interpret experimental evidences on existence of microscopic solitons, and their determining role in electronic processes of quasi-1D electronic crystals. Thus, the ferroelectric charge ordering in organic conductors gives access to several types of solitons observed in conductivity (holons) and in permittivity (polar kinks), to solitons’ bound pairs in optics, to compound charge-spin solitons. In charge density waves, the individual phase solitons have been visually captured in recent STM experiments. The resolved subgap tunneling spectra recover these solitons (in aggregated form of dislocations in statics and as instantons—the phase slips in dynamics), as well as the amplitude kinks—the spinons. The theory relies upon the regime of quantum dissipation provided by soft mode emittance in the course of the soliton creation, and on effects of dimensional crossover. With onset of a 2D or a 3D long range order, the topologically nontrivial solitons experience the confinement resulting in the spin-charge recombination. It originates the symmetry broken spin-or charge- roton configurations with charge- or spin- kinks localized in the core, correspondingly for cases of repulsion and attraction. These complex excitations can be viewed as nucleuses of the melted stripe phases, which appears in doped antiferromagnetic—Mott insulators or in spin-polarized superconductors and charge density waves. [ABSTRACT FROM AUTHOR]

In this paper we present some results related to nonlinear ultrasonic propagation in air-water mixtures. The model we use is based on the coupling of the bubble equation in a volume formulation to the linear wave equation. The main hypothesis are the consideration of adiabatic behavior of the air inside the bubble, uniform size of bubbles, and that the nonlinear behavior comes exclusively from the bubble vibration. Several cases are considered, including continuous and pulsed waves; soliton propagation is also analyzed. Some results considering one bubbly layer are given as well. Finally, a model for standing waves in a cavity is shown. The different numerical algorithms are including in the code SNOW (SNOW-BL). [ABSTRACT FROM AUTHOR]

Valeriy Grikurov passed away on February 15, 2008. We published the brief thesis of the lecture he presented during the Conference Workshop. He had a lot of plans for collaboration with our University. I am sure that somewhere and somehow these plans will be accomplished. Klaudia Oleschko. [ABSTRACT FROM AUTHOR]

The theory of solitons in polyacetylene chains is reviewed with the emphasis on the force that drives the phenomenon. Then, the origin of bifurcation schemes in non-equilibrium thermodynamics is summarized. Examples of bifurcations schemes and of chaotic behaviors in quantum chemical calculations are given. [ABSTRACT FROM AUTHOR]

A gaseous Bose-Einstein condensate (BEC) offers an ideal testing ground for studying symmetry breaking, because a trapped BEC system is in a mesoscopic regime, and situations exist under which symmetry breaking may or may not occur. Investigating this problem can explain why mean-field theories have been so successful in elucidating gaseous BEC systems and when many-body effects play a significant role. We substantiate these ideas in four distinct situations: namely, soliton formation in attractive BECs, vortex nucleation in rotating BECs, spontaneous magnetization in spinor BECs, and spin texture formation in dipolar BECs. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

Propagation of bulk solitary density waves is studied in lengthy elastic wave guides, which have strong dispersion and are made of polymers with remarkable linear dissipation, that leads to decay of any of linear or shock waves at short distances. Nonlinear elasticity of materials results in generation of strain solitons even under short-run and reversible (elastic) loading. Theoretical and experimental research has been performed to prove the existence of long bulk strain solitary waves produced by a laser-induced impact in nonlinearly elastic isotropic wave guides. New experiments in lengthy bars (over 0.5 m) confirm that bulk solitons do not reveal any considerable amplitude decay and shape transformation, while linear or shock waves disappear at much shorter distance completely. Decrement values are small, indeed, and estimated first for elastic nonlinear strain waves dissipation in polymeric bars. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

Korteweg-de Vries (KdV) and Benjamin-Ono (BO) equations are often cited as time-domain models for nonlinear Rayleigh waves in a dispersive medium such as a coated substrate. However, these canonical equations do not account for the nonlocal nonlinearity that is a hallmark of surface acoustic waves. In this paper, a time-domain evolution equation derived for nonlinear Rayleigh waves in nondispersive isotropic media [Hamilton, Il’insky, and Zabolotskaya, J. Acoust. Soc. Am. 97, 891–897 (1995)] is extended to include dispersion due to thin-film coating. It is demonstrated that a class of soliton-like solutions resembling Mexican hats satisfies the evolution equation for the case of KdV-type dispersion, a result obtained previously by Eckl et al. [Phys. Rev. E 70, 046604 (2004)] from a frequency-domain form of the evolution equation. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

Recent results on BPS solitons in the Higgs phase of supersymmetric (SUSY) gauge theories with eight supercharges are reviewed. For U(NC) gauge theories with the NF(> NC) hypermultiplets in the fundamental representation, the total moduli space of walls are found to be the complex Grassmann manifold SU(NF)/[SU(NC) × SU(NF - NC) × U(1)]. The monopole in the Higgs phase has to accompany vortices, and preserves a 1/4 of SUSY. We find that walls are also allowed to coexist with them. We obtain all the solutions of such 1/4 BPS composite solitons in the strong coupling limit. Instantons in the Higgs phase is also obtained as 1/4 BPS states. As another instructive example, we take U(1) × U(1) gauge theories with four hypermultiplets. We find that the moduli space is the union of several special Lagrangian submanifolds of the Higgs branch vacua of the corresponding massless theory. We also observe transmutation of walls and repulsion and attraction of BPS walls. This is a review of recent works on the subject, which was given at the conference by N. Sakai. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

Supersymmetric U(NC) gauge theory with NF massive hypermultiplets in the fundamental representation admits various BPS solitons like domain walls and their webs. In the first part we show as a review of the previous paper that domain walls are realized as kinky fractional D3-branes interpolating between separated D7-branes. In the second part we discuss brane configurations for domain wall webs. This is a contribution to the conference based on the talk given by MN. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

The Sagdeev potential method is used to investigate the non-linear propagation of the dust-acoustic wave in a weakly non-ideal dusty plasma comprising a negatively charged dust fluid, Boltzmann electrons and non-thermal ions which are characterised by a non-thermal parameter α. The non-ideal effects of volume reduction and attractive cohesive forces are introduced by adopting the van der Waal’s equation of state for the dust fluid. Both supersonic and subsonic solitons are found to exist for a non-ideal dusty plasma and comparisons are made with the ideal case. The upper limit of the range of values of the non-thermal parameter for which soliton solutions are admissible, is examined as a function of the non-ideal parameters. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

Experimental data from the 2m propane bubble chamber have been analyzed to search for an exotic baryon states, in the Ks0p, Ks0Λ and Λp decay mode for the reaction p+C3H8 at 10 GeV/c. In the invariant mass spectrum ΛKs0 narrow peaks are observed at 1750, 1795, 1850 MeV/c2. The statistical significance of these peaks has been estimated as 5.6, 3.3 and 3.0 S.D., respectively. There are small enhancements in mass regions of (1650–1675) and (1925–1950) MeV/c2. These would be candidates for the N0 or the [cap_xi]0 pentaquark states. The pKs0 invariant mass spectrum shows resonant structures with MKs0p=1540, 1613, 1821 MeV/c2. The statistical significance of these peaks have been estimated as 5.5,4.8 and 5.0 s.d., respectively. There are also small peaks in 1487 (3 s.d.), 1690 (3.6 s.d.), 1750 (2.3 s.d.) and 1980 (3.0 s.d.) MeV/c2 mass regions. In the invariant mass spectrum S=-1 Λp narrow peaks at 2100, 2175, 2285 and 2353 MeV/c2 are observed. Their excess above background by the second method is 6.9, 4.9, 3.8 and 2.9 S.D., respectively. There is also a small peak in 2225 (2.2 s.d.) MeV/c2 mass region. The investigation has been performed at the Veksler and Baldin Laboratory of High Energies, JINR. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

In this paper, the 2D stationary-propagating localized solutions of Boussinesq’s equation are investigated numerically. An algorithm for treating the bifurcation and finding a nontrivial solution is created. The scheme is validated employing different grid sizes and different size of the box that contains the solution. The results obtained show that there is pseudo-Lorentzian elongation of the scale of the solitons but it is only in the direction transverse to the propagation velocity. In longitudinal direction the scales are slightly contracted, so kind of “relative” contraction takes place. Results are shown graphically and discussed. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

The Hirota Method, with modified background is applied to construct exact analytical solutions of nonlinear reaction-diffusion equations of two types. The first equation has only nonlinear reaction part, while the second one has in addition the nonlinear transport term. For both cases, the reaction part has the form of the third order polynomial with three distinct roots. We found analytic one-soliton solutions and the relationships between three simple roots and the wave speed of the soliton. For the first case, if one of the roots is the mean value of other two roots, the soliton is static. We show that the restriction on three distinct roots to obtain moving soliton is removed in the second case by, adding nonlinear transport term to the first equation. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

The nonlinear properties of metamaterials are going to be important for the control of new computing and sensor devices. In addition, an exciting dimension can be added through the inclusion of magnetooptical properties. Both temporal and spatial solitons will be considered for a range of metamaterials with an emphasis being placed upon bright and bright-dark soliton interactions coupled to magnetic effects drawn from both the Voigt and the Faraday configurations. Strongly nonlinear waves will also be discussed in terms of their exciting ability to slow light and respond vigorously to both nonlinear and magnetooptic tuneability. A special emphasis will be placed upon the switching possibilities of solitons at an interface and complex waveguides, and shape effects will also be addressed. [ABSTRACT FROM AUTHOR]