Explicit formulae for the inverse of an interval matrix of the form [I − ∆, I + ∆] (where I is the unit matrix) are proved via finding explicit solutions of certain nonlinear matrix equations.

Explicit formulae for the inverse of an interval matrix of the form [I − ∆, I + ∆] (where I is the unit matrix) are proved via finding explicit solutions of certain nonlinear matrix equations.

Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with 2 × 2 matrix or second order scalar spectral problems. The theory is illustrated by derivation of the Whitham equations for perturbed Korteweg-de Vries equation and nonlinear Schrödinger equation with linear damping.

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

where N ≥ 3, p ∈ ( 1, N+2 N−2 ) , V : R → R, J : R → RN×N are C functions. Here the symbol RN×N stands for the set of (N ×N) real matrices. Such a problem, at least in the case J ≡ I, where I is the identity matrix in RN×N , arises naturally when seeking standing waves of the nonlinear ∗Supported by MIUR, national project Variational methods and nonlinear differential equations †Supported by MI...

in this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. periteration this method requires three evaluations of the function and one evaluation of its first derivative. a general error analysis providing the eighth order of convergence is given. several numerical examples are given to illustrate the efficiency and performance of the new ...

Keywords: Systems of nonlinear delay differential equations Time-varying delays Global stability M-matrix BAM neural network Leakage delays a b s t r a c t We consider a nonlinear non-autonomous system with time-varying delays

Output regulation of neutral type nonlinear systems is considered. Regulator equations are derived, which generalize Francis-Byrnes-Isidori equations to the case of neutral systems. It is shown that, under standard assumptions, the regulator problem is solvable if and only if these equations are solvable. In the linear case, the solution of these equations is reduced to linear matrix equations.

Using matrix identities, we construct explicit pseudo-exponential-type solutions of linear Dirac, Loewner and Schrödinger equations depending on two variables and of nonlinear wave equations depending on three variables.