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This paper studies the Davey–Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis. [ABSTRACT FROM PUBLISHER]

An innovative method for fast analysis of electromagnetic problems comprising nonlinear dielectrics is proposed. The method is based on the combination of finite elements and domain decomposition methods. This latter technique allows for the separation of the problem in multiple subproblems which can be solved separately. By appropriately defining one of such subdomains as containing all the nonlinear dielectrics it is possible to restrict the application of an iterative algorithm for the numerical solution of nonlinear equations only to this latter, smaller, domain. Numerical results showing the accuracy and efficiency of this technique are presented in few 2D cases. [ABSTRACT FROM AUTHOR]

We show that spin-squeezing implies entanglement for the quantum tripartite state, where the subsystem of the bipartite state is identical. We study the relation between spin-squeezing parameters and entanglement through the quantum entropy of a system, starting initially in a pure state when the cavity is binomial. We show that spin-squeezing can be a convenient tool to give some insight into the subsystems entanglement dynamics when the bipartite subsystem interacts simultaneously with the cavity field subsystem, especially when the interaction occurs off-resonantly without and with a nonlinear medium contained in the cavity field subsystem. We illustrate that, in the case of large off-resonance interaction, spin-squeezing clarifies the properties of entanglement almost with full success. However, it is not a general rule when the cavity is assumed to be filled with a nonlinear medium. In this case, we illustrate that the insight into entanglement dynamics becomes more clear in the case of a weak nonlinear medium than in strong nonlinear medium. In parallel, the role of the phase-space distribution in quantifying entanglement is also studied. The numerical results of Husimi Q-function show that the integer strength of the nonlinear medium produces Schrödinger cat states, which is necessary for quantum entanglement. [ABSTRACT FROM AUTHOR]

We present a detailed account of theoretical and experimental studies of nonlinear molecular photonic processes accompanying the propagation of short intense laser pulses through an organic liquid cored fiber array. The theory takes into account two-photon absorption, excited state absorption, and dynamical evolution of the molecular energy level populations and the laser intensity. The coupled dynamical equations for the molecular energy-level populations and laser intensity are solved numerically using experimentally observed molecular and optical parameters. Experimentally obtained optical limiting results are analyzed along with nonlinear absorption and pump-probe studies of other nonlinear optical processes occurring in the fiber core. It is found that in the nanosecond time regime, besides excited state and two-photon absorption, thermal and density effects also contribute significantly to the optical limiting performance of the constituent fiber [ABSTRACT FROM PUBLISHER]

A rigorous mathematical model of nonlinear, parametric interactions of microwave magnetostatic dipole-dipole waves and electro-magnetic waves in 3-D ferrite films in waveguiding structures is developed. The 3-D nonlinear diffraction boundary problem of the full nonlinear Maxwell's equations with electrodynamical boundary conditions, complemented by the Landau-Lifshitz equation (without the exchange term) is solved. The instability of parametric excitation process of magnetostatic waves in 3-D ferrite structures is simulated by the numerical method of bifurcation analysis of the nonlinear Maxwell's operator for the 3-D boundary problem. The results show discrete maxima in the magnitude of reflected electromagnetic waves for distinct ferrite thickness values in the 1 ~m to 1 mm range. The mode profiles were obtained. The instability regions, depending on the bifurcation parameters, were determined, and shown to be more sensitive to the pumping power than the parametric excitation of electromagnetic waves alone. [ABSTRACT FROM AUTHOR]

A new approach based on the bifurcation theory to develop mathematical models of nonlinear electromagnetic waves and oscillations in waveguiding and resonator structures, containing a strongly nonlinear bounded gyromagnetic medium, is proposed. A new method for rigorous modeling of nonlinear phenomena due to the instability in the three-dimensional ferrite structures was developed based on the numerical analysis of the bifurcation points of the nonlinear Maxwell's operator. The bifurcation points were determined by our computational algorithm, using the eigenvalues of the matrix resulting from the linearized Maxwell's operator. The onset and the breakdown of self-oscillations in the ferrite resonator structure, caused by the instability, were modeled. The transition regime from regenerative parametric amplification to parametric generation, depending on the magnitude of the pumping wave and resonator detuning, was simulated infinitesimally close to the bifurcation points. [ABSTRACT FROM AUTHOR]