相关论文: The short pulse equation is integrable

We prove the integrability of the short pulse equation derived recently by Sch\"afer and Wayne from a hamiltonian point of view. We give its bi-hamiltonian structure and show how the recursion operator defined by the hamiltonian operators…

We consider the ultrashort light pulse propagation through an inhomogeneous monomodal optical fiber exhibiting higher-order dispersive effects. Wave propagation is governed by a generalized nonlinear Schr\"{o}dinger equation with varying…

From a columnar approximation of the Euler equations of an incompressible fluid with surface tension, we derive in the short-wave approximation a new integrable classical 1+1 dimensional field theory for the motion of the surface. Together…

The propagation of optical pulses in two types of fibers with randomly varying dispersion is investigated. The first type refers to a uniform fiber dispersion superimposed by random modulations with a zero mean. The second type is the…

We consider three novel PDEs associated with the integrable generalizations of the short pulse equation classified recently by Hone {\it et al} (2018 {\it Lett. Math. Phys.} {\bf 108} 927-947). In particular, we obtain a variety of exact…

We study the interband self-induced transmission of surface plasmon polaritons in a gold film surrounded by an external Kerr medium. We model the optical propagation by using a version of the generalized nonlinear Schrodinger equation for…

We derive coupled propagation equations for ultrashort pulses in a degenerate three-wave mixing process in quadratic media, using approximations consistent with the slowly evolving wave approximation [T. Brabec and F. Krausz, Phys. Rev.…

The propagation of light-pulse with negative group-velocity in a nonlinear medium is studied theoretically. We show that the necessary conditions for these effects to be observable are realized in a three-level $\Lambda$-system interacting…

The paper describes a formulation of discrete scalar wave propagation in an inhomogeneous medium by the use of elementary processes obeying a discrete Huygens' principle and satisfying fundamental symmetries such as time-reversal,…

The generalized sine-Gordon (sG) equation was derived as an integrable generalization of the sG equation. In this paper, we develop a direct method for solving the generalized sG equation without recourse to the inverse scattering method.…

Third-order nonlinear dispersion equations (NDEs) are shown to admit both shock and rarefaction waves (as weak solutions), which are distinguished by a smooth deformation approach. Compacton-type travelling wave solutions are proved to be…

The short pulse equation provides a model for the propagation of the ultra-short light pulse in silica optical fibers It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the inhomogeneous initial…

We apply the method of slowly-varying amplitudes of the electrical and magnet fields to integro-differential system of nonlinear Maxwell equations. The equations are reduced to system of differential Nonlinear Maxwell amplitude Equations…

The nonlinear propagation of intense incoherent photons in a photon gas is considered. The photon-photon interactions are governed by a pair of equations comprising a wave-kinetic equation for the incoherent photons in the presence of the…

The solitary wave solution and periodic solutions expressed in terms of elliptic Jacobi's functions are obtained for the nonlinear Schr\"{o}dinger equation governing the propagation of pulses in optical fibers including the effects of…

The well-known (1+1D) nonlinear Schr\"odinger equation (NSE) governs the propagation of narrow-band pulses in optical fibers and others one-dimensional structures. For exploration the evolution of broad-band optical pulses (femtosecond and…

A theoretical study of surface plasmon polaritons (SPPs) in ultrathin lossy metal films is presented. The dispersion relation of such films is well known and can be solved numerically to obtain a combination of long-range (LR-) and…

A novel time domain solver of Maxwell's equations in passive (dispersive and absorbing) media is proposed. The method is based on the path integral formalism of quantum theory and entails the use of ({\it i}) the Hamiltonian formalism and…

We present a comprehensive framework for treating the nonlinear interaction of few-cycle pulses using an envelope description that goes beyond the traditional SVEA method. This is applied to a range of simulations that demonstrate how the…

The system of equations describing an ultrashort optical pulses propagation in semiconductor superlattice with applied magnetic field was obtained based on Boltzmann equation in the relaxation-time approximation for the single electron…