sufficient conditions are established under which the zero solution x = 0 of equation (2) isunstable.

solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modied korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

for non-darcy flow in submerged porous media a one- dimensional mathematical model has been developed. rockfill detention dams are one of these porous media that comprised of relatively homogenous coarse rockfill which can be used to reduce flood discharge and hydrograph peak. in this research the focus was on the rockfill detention dams in submerged condition. the existence of overtopping rock...

in current work a comprehensive mechanism based on intermediate radical termination theory is assumed for raft polymerization of styrene over cumyl dithiobenzoate as raft agent. rate constants for addition (ka) and fragmentation reactions (kf) are set to 6×106 and 5×104 respectively, which lead to an equilibrium constant value of k = ka/kf = 1.2 x 102. moment equations method was used to model ...

in this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (dtm). this is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. several numerical examples are given and by comparing the numerical results obtained from dtm  and  predi...

‎we study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{r}}^2$ with critical exponential growth‎. ‎this model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

in this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $e=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...

in this article we study steensen method to solve nonlinear matrix equation x+a^t x^(-1) a=q, when a is a normal matrix. we establish some conditions that generate a sequence of positive denite matrices which converges to solution of this equation.

most developing countries have achieved productivity growth in economic sectors like agriculture for more than 30 years. universities and governmental research centers have tried to generate knowledge with direct social and economic effects during these decades. so, productivity and production growth can be attributed to technological changes made possible through investment in agricultural res...

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...