In this work, the issue of favorable numerical methods for the space and time discretization of low-dimensional nonlinear Schrödinger equations is addressed. The objective is to provide a stability and error analysis of high-accuracy discretizations that rely on spectral and splitting methods. As a model problem, the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Ei...

Let gl(n, R) be the Lie algebra consisting of all n × n matrices over a commutative ring R with identity 1. In this paper, we prove that every generalized Lie triple derivation of gl(n, R)(n ≥ 2) is the sum of a Lie triple derivation and a homothety.

Cyclotron resonant wave-particle interactions are studied in the context of Hamiltonian theory with utilization of Lie transform techniques. The canonical perturbation method for single particle motion is used for providing results for the collective particle behavior under interaction with wave fields of either localized or periodic profiles. Analytical expressions for the calculation of phase...

the complete 3d nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. for describing the dynamics of the system, the newtonian derivation procedure is followed. the velocity field inside the pipe formulated using hydrostatic and bernoulli equations. the hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in var...

The aim of this article is to discuss the n-derivation algebras Lie color algebras. It proved that, if base ring contains 1/n-1, L a perfect algebra with zero center, then every triple derivation derivation, and nDer(L)) an inner derivation.

An Einstein nilradical is a nilpotent Lie algebra, which can be the nilradical of a metric Einstein solvable Lie algebra. The classification of Riemannian Einstein solvmanifolds (possibly, of all noncompact homogeneous Einstein spaces) can be reduced to determining, which nilpotent Lie algebras are Einstein nilradicals and to finding, for every Einstein nilradical, its Einstein metric solvable ...

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...