Related papers: Soliton solutions in the class of implicit differe…
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
The goal of this work is to determine classes of traveling Solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz.
We propose a new type of soliton equation, which is obtained from the generalized discrete BKP equation. The obtained equation admits two types of soliton solutions. The signs of amplitude and velocity of the soliton solution are opposite…
In this paper, we study nonlinear differential equations arising from Eulerian polynomials and their applications. From our study of nonlinear differential equations, we derive some new and explicit identities involving Eulerian and…
Existence of a new class of soliton solutions is shown for higher order nonlinear Schrodinger equation, describing thrid order dispersion, Kerr effect and stimulated Raman scattering. These new solutions have been obtaiened by invoking a…
The behaviour of solitons in integrable theories is strongly constrained by the integrability of the theory; i.e. by the existence of an infinite number of conserved quantities which these theories are known to possess. One usually expects…
Recently it has been discovered that some nonlinear evolution equations in 2+1 dimensions, which are integrable by the use of the Spectral Transform, admit localized (in the space) soliton solutions. This article briefly reviews some of the…
We present a simple approach for finding $N$-soliton solution and the corresponding Jost solutions of the derivative nonlinear Scr\"{o}dinger equation with nonvanishing boundary conditions. Soliton perturbation theory based on the inverse…
This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including a quasi-Fermat theorem and a quasi-Mean Value Theorem. As an application, this paper develops several numerical…
We consider several ways of how one could classify the various types of soliton solutions related to nonlinear evolution equations which are solvable by the inverse scattering method. In doing so we make use of the fundamental analytic…
In this paper we are interested in the numerical solution of stochastic differential equations with non negative solutions. Our goal is to construct explicit numerical schemes that preserve positivity, even for super linear stochastic…
We determine a considerable class of nonlinear partial differential equation systems which have global regular solutions. Uniqueness is not a direct general consequence of this method. The scheme can be applied to the incompressible Navier…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
Although most soliton research has traditionally considered dominant quadratic dispersion, the recent discovery of pure-quartic solitons has inspired analysis of soliton solutions with large higher orders of dispersion. Here we present…
Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr\"oinger equation respectively. Multi-soliton solutions of the resulted…
We investigate the first order implicit linear difference equation over residue class rings modulo m. We prove an existence criterion and establish the amount of solutions for this equation. We obtain analogous results for the initial…
In this paper, we study nonlinear differential equations satisfied by the generating function of Boole numbers. In addition, we derive some explicit and new interesting identities involving Boole numbers and higher-order numbers arising…
We analyse the structure of the exact, dark and bright soliton solutions of the driven non-linear Schr\"odinger equation. It is found that, a wide class of solutions of the higher order non-linear Schr\"odinger equation with a source can…
We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that…