The paper represents the method for construction of the families of particular solutions to some new classes of (n + 1) dimensional nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE. Admittable solutions depend on arbitrary functions of n variables.

this research presents a numerical tool to estimate the green's function operator matrix of intraplate faults. having this matrix and its inverse, spatial distribution of fault slippage could be investigated through the inverse analysis of geodetic data. this information could be employed to predict the location of future powerful earthquakes. to implement fault sliding in fe calculations,...

Adjoint symmetry constraints are presented to manipulate binary nonlinearization, and shown to be a slight weaker condition than symmetry constraints in the case of Hamiltonian systems. Applications to the multicomponent AKNS system of nonlinear Schrödinger equations and the multi-wave interaction equations, associated with 3×3 matrix spectral problems, are made for establishing their integrabl...

The paper represents the method for construction of the families of particular solutions to some new classes of (n + 1) dimensional nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE. Admittable solutions depend on arbitrary functions of n variables.

Nonlinear state-space models driven by differential equations have been widely used in science. Their statistical inference generally requires computing the mean and covariance matrix of some nonlinear function of the state variables, which can be done in several ways. For example, such computations may be approximately done by Monte Carlo, which is rather computationally expensive. Linear appr...

We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM). Nonlinear stiffness matrices are constructed usingGreen-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the di...

this paper proposes a three-step method for solving nonlinear volterra integralequations system. the proposed method convents the system to a (3 × 3)nonlinear block system and then by solving this nonlinear system we ndapproximate solution of nonlinear volterra integral equations system. to showthe advantages of our method some numerical examples are presented.

This paper proposes sufficient conditions to the regional stability analysis of switched nonlinear systems with time-varying parameters. The nonlinear sub-modes of operation are described by means of differential-algebraic equations involving the state and an auxiliary nonlinear vector. We then use piecewise polynomial Lyapunov functions and a relaxation technique that lead to a convex characte...

Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix solutions of the defocusing nonlinear Schrödinger equation with quasi-analytic boundary conditions is dealt with. (The result is new even for a scalar nonline...

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...