We consider a class of one dimensional vector Non-linear Schr$\ddot{o}$dinger Equation(NLSE) in an external complex potential with Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components field. The solvability generic system is investigated for various combinations time modulated LC BLG terms, space-time dependent strength nonlinear interaction potential. use non-unitary transforma...

We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler’s method the equation is split into a linear stochastic equation and a non-linear random evolution equation. The linear stochastic equation is discretized in space by a non-adaptive wavelet-Galerkin method. This equation is solved first and its solution is substituted into the non...

We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler’s method the equation is split into a linear stochastic equation and a non-linear random evolution equation. The linear stochastic equation is discretized in space by a non-adaptive wavelet-Galerkin method. This equation is solved first and its solution is substituted into the non...

This study is concerned to check the validity and applicability of a five parameter viscoelastic model for harmonic wave propagating in the non-homogeneous viscoelastic rods of varying density. The constitutive relation for five parameter model is first developed and validity of these relations is checked. The non-homogeneous viscoelastic rods are assumed to be initially unstressed and at rest....

In this paper homotopy perturbation method (HPM) is employed to solve two kinds of differential equations: one dimensional non homogeneous parabolic partial differential equation and non linear differential equation. Using the HPM, an exact analytical solution to non homogeneous parabolic partial differential equation and an approximate explicit solution for a non linear differential equation w...

This paper deals with state estimation of micro tunable capacitor subjected to nonlinear electrostatic force. For this end a nonlinear observer has been designed for state estimation of the structure.  Necessary and sufficient conditions for construction of the observer are presented. Stability of the observer is checked using Lyapunov theorem. Observer design is based on converting of differen...

A new approach to high energy evolution based on a linear equation for QCD generating functional is developed. This approach opens a possibility for systematic study of correlations inside targets, and, in particular, inside realistic nuclei. Our results are presented as three new equations. The first one is a linear equation for QCD generating functional (and for scattering amplitude) that sum...

accurate and nondestructive methods to determine individual leaf areas of plants are useful tools in physiological and agronomic research. a determination of the individual leaf area (la) of such species in brassicaceae family as red cabbage (brassica oleracea var. cappitata l. f. rabra), cabbage (brassica oleracea var. cappitata l. f. alba) and broccoli (brassica oleracea var. italica l.) ...