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Nonisospectral integrable systems can describe solitary waves in nonuniform media. In this paper, we apply the Cauchy matrix approach to construct three types of nonisospectral matrix modified Korteweg-de Vries (mKdV) eqautions and present…
Warped compactifications with branes provide a new approach to the hierarchy problem and generate a diversity of four-dimensional thresholds. We investigate the relationships between these scales, which fall into two classes. Geometrical…
We derive the perturbative four-dimensional effective theory describing heterotic M-theory with branes and anti-branes in the bulk space. The back-reaction of both the branes and anti-branes is explicitly included. To first order in the…
In this paper we consider $(n+1)$-dimensional cosmological model with scalar field and antisymmetric $(p+2)$-form. Using an electric composite $Sp$-brane ansatz the field equations for the original system reduce to the equations for a…
We study a class of noncanonical real scalar field models in $(1+1)$-dimensional flat space-time. We first derive the general criterion for the classical linear stability of an arbitrary static soliton solution of these models. Then we…
We formulate a six dimensional $U(1)$ gauge theory compactified on a (two dimensional) sphere $S^2$ with flux and localized brane sources. Profiles of the lowest Kaluza-Klein (KK) wavefunctions and their masses are derived analytically. In…
We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties.…
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature…
The unimodular version of the Kaluza-Klein theory is briefly recalled, and its projection on the $4$-dimensional spacetime is constructed. Imposing unimodularity condition on the $5$-dimensional Kaluza-Klein metric, det$g_{AB}=1$ is…
A toy model where a massless, real, scalar field $\Phi$ in a compact space-time ${\cal M}_4 \times {\cal S}_1$ is coupled to a brane (parametrized as a $\delta$-function) through the unique relevant operator $\delta (y) \Phi^2 (x,y)$ is…
The quantum Yang-Baxter equation is a braiding condition on vector spaces which is of high relevance in several fields of mathematics, such as knot theory and quantum group theory. Their combinatorial counterpart are set-theoretic solutions…
In this paper we discuss the construction of non-geometric Q- and R-branes as sources of non-geometric Q- and R-fluxes in string compactifications. The non-geometric Q-branes, being obtained via T-duality from the NS 5-brane or respectively…
We consider an internal space of two discrete points in the fifth dimension of the Kaluza-Klein theory by using the formalism of noncommutative geometry developed in a previous paper \cite{VIWA} of a spacetime supplemented by two discrete…
We consider `brane universe' scenarios with standard-model fields localized on a 3-brane in 6 spacetime dimensions. We show that if the spacetime is rotationally symmetric about the brane, local quantities in the bulk are insensitive to the…
This work deals with the presence of defect structures in models described by real scalar field in a diversity of scenarios. The defect structures which we consider are static solutions of the equations of motion which depend on a single…
The equations describing the Kaluza-Klein reduction of conformally flat spaces are investigated in arbitrary dimensions. Special classes of solution related to pseudo-Kahler and para-Kahler structures are constructed and classified…
We present a brief description of noncompactified higher-dimensional theories from the perspective of general relativity. More concretely, the Space-Time-Matter theory, or Induced Matter theory, and the reduction procedure used to construct…
We discuss theories in which the standard-model particles are localized on a brane embedded in space-time with large compact extra dimensions, whereas gravity propagates in the bulk. In addition to the ground state corresponding to a…
This paper investigates the algebraic reduction of the infinite-dimensional symmetries of the Ablowitz-Kaup-Newell-Segur system when restricted to multi-soliton solution. By systematically analyzing, we demonstrate that the entire…
We examine the Kaluza-Klein theory for warped flux compactifications of type $II\ b $ string theory on a Minkowski spacetime $ M_4$ times a conic Calabi-Yau orientifold $X_6$. The region glued along the internal space directions to the bulk…