In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in...

generally, this article deals with the challenges and solutions facing the internet security. first, the article discusses the following subjects: the security of communication and information networks, the importance of the networks, the networks security precedence internet and computers crimes, the beginning of computer crimes, classifying computer crimes as well as the solutions proposed to...

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

A careful exposition of Zilber’s quasiminimal excellent classes and their categoricity is given, leading to two new results: the Lω1,ω(Q)definability assumption may be dropped, and each class is determined by its model of dimension א0. Boris Zilber developed quasiminimal excellent classes in [Zil05], in order to prove that his conjectural description of complex exponentiation was categorical. T...

‎using variational arguments‎, ‎we prove the existence of infinitely‎ ‎many solutions to a class of $p$-biharmonic equation in‎ ‎$mathbb{r}^n$‎. ‎the existence of‎ ‎nontrivial‎ ‎solution is established under a new‎ ‎set of hypotheses on the potential $v(x)$ and the weight functions‎ ‎$h_1(x)‎, ‎h_2(x)$‎.

we derive the formulas of the maximal andminimal ranks of four real matrices $x_{1},x_{2},x_{3}$ and $x_{4}$in common solution $x=x_{1}+x_{2}i+x_{3}j+x_{4}k$ to quaternionmatrix equations $a_{1}x=c_{1},xb_{2}=c_{2},a_{3}xb_{3}=c_{3}$. asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. we give the exp...

We show analytically and numerically the existence of double vortex solutions in two-Higgs systems. These solutions are generalizations of the Nielsen-Olesen vortices and exist for all values of the parameters in the Lagrangians considered. We derive analytically the asymptotic behavior of the solutions and confirm it numerically by solving the field equations. Finally, we show that these solut...