Related papers: Soliton and Periodic solutions of the Short Pulse …
We investigate an influence of the random external electric field on the 2D extremely short optical pulses propagation in the silicene. The random electric field is perpendicular to the silicene plane. An effective equation has the form of…
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…
Traveling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be approximated by solitons of an effective nonlinear Schrodinger…
We consider the long-time behavior of solutions to the short-pulse equation. Using the method of testing by wave packets, we prove small data global existence and modified scattering.
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc.. The stable solitons have been captured not only…
We propose a multi-component generalization of the modified short pulse (SP) equation which was derived recently as a reduction of Feng's two-component SP equation. Above all, we address the two-component system in depth. We obtain the Lax…
We propose new type of discrete and ultradiscrete soliton equations, which admit extended soliton solution called periodic phase soliton solution. The discrete equation is derived from the discrete DKP equation and the ultradiscrete one is…
The polysymplectic analysis of the Short Pulse Equation known in nonlinear optics is used in order to construct a geometric polysymplectic integrator for it. The proposed scheme turns out to be much more effective than other standard…
We study an intense-short pulse propagation in a saturable cubic-quintic nonlinear media in the presence of nonlinear dispersion within the framework of an extended variational approach. We derive an effective equation for the pulse width…
Surface plasmon polaritons (SPP or SP) are electromagnetic waves propagating along metal dielectric interfaces and existing over a wide range of frequencies. They have become popular because of their sub-wavelength confinement and the…
In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key of the construction is the bilinear forms and determinant structure of solutions of the CSP…
In the present paper, we mainly study the integrable semi-discretization of a multi-component short pulse equation. Firstly, we briefly review the bilinear equations for a multi-component short pulse equation proposed by Matsuno (J. Math.…
We propose an integrable system of coupled nonlinear Schrodinger equations with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short optical soliton pulse propagation in non-Kerr media. Lax pair, conserved…
In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semilinear evolution problems on the real line with spatially…
Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations -- including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single…
We rigorously analyze the asymptotics of soliton gases to the short-pulse (SP) equation. The soliton gas is formulated in terms of a RH problem, which is derived from the RH problems of the $N$-soliton solutions with $N \to \infty$.…
We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a defocusing nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the…
We consider the evolution of ultra-short optical pulses in linear and nonlinear media. For the linear case, we first show that the initial-boundary value problem for Maxwell's equations in which a pulse is injected into a quiescent medium…
We investigate the propagation of an ultrashort optical pulse using Fokas-Lenells equation (FLE) under varying dispersion, nonlinear effects and perturbation. Such a system can be said to be under soliton management (SM) scheme. At first,…
The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing wave spacetimes and then extracts approximate solutions of the physical problem, with…