Related papers: Integrable semi-discretization of a multi-componen…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
In this paper we present a reduction technique based on bilinearization and double Wronskians (or double Casoratians) to obtain explicit multi-soliton solutions for the integrable space-time shifted nonlocal equations introduced very…
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide…
We propose a technique of compensating the spurious reflections implied by the multiple-scattering (MS) method, commonly used for analyzing finite photonic crystal (PC) systems, to obtain exact values of characteristic parameters, such as…
We investigate the soliton dynamics for the fractional nonlinear Schrodinger equation by a suitable modulational inequality. In the semiclassical limit, the solution concentrates along a trajectory determined by a Newtonian equation…
In this paper a new semi-implicit relaxation scheme for the simulation of multi-scale hyperbolic conservation laws based on a Jin-Xin relaxation approach is presented. It is based on the splitting of the flux function into two or more…
The reciprocal link between the reduced Ostrovsky equation and the $A_2^{(2)}$ two-dimensional Toda system is used to construct the $N$-soliton solution of the reduced Ostrovsky equation. The $N$-soliton solution of the reduced Ostrovsky…
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable…
A kind of spatial fractional diffusion equations in this paper are studied. Firstly, an L1 formula is employed for the spatial discretization of the equations. Then, a second order scheme is derived based on the resulting semi-discrete…
Hirota's bilinear method ("direct method") has been very effective in constructing soliton solutions to many integrable equations. The construction of one- and two-soliton solutions is possible even for non-integrable bilinear equations,…
We consider Hamiltonian PDEs that can be split into a linear unbounded operator and a regular non linear part. We consider abstract splitting methods associated with this decomposition where no discretization in space is made. We prove a…
A three- and five-component nonlinear Schrodinger-type models, which describe spinor Bose-Einstein condensates (BEC's) with hyperfine structures F=1 and F=2 respectively, are studied. These models for particular values of the coupling…
The interaction of a weakly bound Rydberg electron with an electromagnetic half-cycle pulse (HCP) is described with the help of a multidimensional semiclassical treatment. This approach relates the quantum evolution of the electron to its…
In this work, we employ the generalized perturbation reduction method to find the two-component vector breather solution of the cubic Boussinesq equation $U_{tt} - C U_{zz} - D U_{zzzz}+G (U^{3})_{zz}=0$. Explicit analytical expressions for…
A chain of transformations is found which relates one new integrable case of the generalized short pulse equation of Hone, Novikov and Wang [arXiv:1612.02481] with the sine-Gordon equation.
We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized…
This paper investigates the stability of both the semi-discrete and the implicit central scheme for the linear damped wave equation on the half-line, where the spatial boundary is characteristic for the limiting equation. The proposed…
On the basis of a recently-proposed method to find solitary solutions of generalized nonlinear Schrodinger equations [1]-[3], the existence of an envelope solitonlike solutions of a nonlinear Schrodinger equation containing an anti-cubic…
The distinctive features of passing the two-component extremely short pulses through the nonlinear media are discussed. The equations considered describe the propagation in the two-level anisotropic medium of the electromagnetic pulses…
This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such…