We show that there exist maximal globally hyperbolic solutions of the Einstein-dust equations which admit a constant mean curvature Cauchy surface, but are not covered by a constant mean curvature foliation.

A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bilinear and commutative mapping on the solution space, is studied. This family of PDE’s contains the Cauchy–Riemann equations and the cofactor pair systems, included as special cases. The multiplication provides a method for generating, in a pure algebrai...

defines a solution of the generalized WDVV-system (1). Of course other gauge groups may be considered and more general solutions may be proposed for classical Lie groups [3, 4]. So although extremely difficult to solve in general, this overdetermined system of nonlinear equations admit exact solutions. In this note we shall present a complete proof that a substantial class of solutions for the ...

In this letter we propose an approach to obtain solutions for the nonlocal nonlinear Schrödinger hierarchy from the known ones of the Ablowitz-Kaup-Newell-Segur hierarchy by reduction. These solutions are presented in terms of double Wronskian and some of them are new. The approach is general and can be used for other systems with double Wronskian solutions which admit local and nonlocal reduct...

We utilize the classification of IIB horizons with 5-form flux to present a unified description for the geometry of AdSn, n = 3, 5, 7 solutions. In particular, we show that all such backgrounds can be constructed from 8-dimensional 2-strong CalabiYau geometries with torsion which admit some additional isometries. We explore the geometry of AdS3 and AdS5 solutions but we do not find AdS7 solutions.

The invariant subspace method is used to classify a class of systems of nonlinear dispersive evolution equations and determine their invariant subspaces and exact solutions. A crucial step is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that systems of evolution equations admit. A few examples of presenting exact solutions with generalized sepa...

It is shown that some known solutions of Einstein’s vacuum field equations admit null infinities such that the sections of the null hypersurface at infinity are toroidal. PACS numbers: 0420G, 0420H, 0430

The paper describes multistage design of composite (modular) systems (i.e., design of a system trajectory). This design process consists of the following: (i) definition of a set of time/logical points; (ii) modular design of the system for each time/logical point (e.g., on the basis of combinatorial synthesis as hierarchical morphological design or multiple choice problem) to obtain several sy...

Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c 0 ∗ > such that for each c c∗ ≥ , the systems under consideration admit monotonic nondecreasing traveling waves.