Using Painlevé analysis, the Hirota multi-linear method and a direct ansatz technique, we study analytic solutions of the (1+1)-dimensional complex cubic and quintic Swift-Hohenberg equations. We consider both standard and generalized versions of these equations. We have found that a number of exact solutions exist to each of these equations, provided that the coefficients are constrained by ce...

Computational modeling of pattern formation in nonequilibrium systems is a fundamental tool for studying complex phenomena biology, chemistry, materials and engineering sciences. The pursuit theoretical descriptions some among those physical problems led to the Swift–Hohenberg equation (SH3) which describes selection vicinity instabilities. A finite differences scheme, known as Stabilizing Corr...

In this paper, we find all the solutions of the Diophantine equation x + 2 513 = y in nonnegative integers x, y, α, β, γ, n ≥ 3 with x and y coprime. In fact, for n = 3, 4, 6, 8, 12, we transform the above equation into several elliptic equations written in cubic or quartic models for which we determine all their {2, 5, 13}-integer points. For n ≥ 5, we apply a method that uses primitive diviso...

an attempt is made for the first time to solve the quadratic and cubic model of magneto hydrodynamic poiseuille flow of phan-thein-tanner (ptt). series solution of magneto hydrodynamic (mhd) flow is developed by using homotopy perturbation method (hpm). results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. the results obtained reveals ma...

The paper is devoted to complete proofs of theorems on consistency on cubic lattices for 3 × 3 determinants. The discrete nonlinear equations on Z defined by the condition that the determinants of all 3×3 matrices of values of the scalar field at the points of the lattice Z that form elementary 3 × 3 squares vanish are considered; some explicit concrete conditions of general position on initial...

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.

We give an error analysis of Strang-type splitting integrators for nonlinear Schrödinger equations. For Schrödinger-Poisson equations with an H4-regular solution, a first-order error bound in the H1 norm is shown and used to derive a second-order error bound in the L2 norm. For the cubic Schrödinger equation with an H4-regular solution, first-order convergence in the H2 norm is used to obtain s...

The paper is devoted to complete proofs of theorems on consistency on cubic lattices for 3 × 3 determinants. The discrete nonlinear equations on Z defined by the condition that the determinants of all 3×3 matrices of values of the scalar field at the points of the lattice Z that form elementary 3 × 3 squares vanish are considered; some explicit concrete conditions of general position on initial...

By making the connection between four-dimensional lattice Green functions (LGFs) and Picard–Fuchs ordinary differential equations of Calabi–Yau manifolds, we have given explicit forms for the coefficients of the fourdimensional LGFs on the simple-cubic and body-centred cubic lattices, in terms of finite sums of products of binomial coefficients, and have shown that the corresponding four-dimens...