Related papers: Grassmanian and Bosonic Thirring Models with Jump …
In this paper we construct the two component supersymmetric generalized Harry Dym equation which is integrable and study various properties of this model in the bosonic limit. In particular, in the bosonic limit we obtain a new integrable…
We present a hybrid Boltzmann-BGK model for inert mixtures, where each kind of binary interaction may be described by a classical Boltzmann integral or by a suitable relaxation-type operator. We allow also the possibility of changing the…
In this paper we study the higher secant varieties of Grassmann varieties in relation to Waring's problem for alternating tensors and to Alexander-Hirschowitz theorem. We show how to identify defective higher secant varieties of…
In this work, we review and clarify computational issues about the W-gauge boson one-loop contribution to the H -> gamma gamma decay amplitude, in the unitary gauge and in the Standard Model. We find that highly divergent integrals depend…
Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…
Two main themes populate this Thesis's pages: transgression forms as Lagrangians for gauge theories and the Abelian semigroup expansion of Lie algebras. A transgression form is a function of two gauge connections whose main property is its…
In this work, we continue the development of methods for constructing Lax pairs and recursion operators for nonlinear integrable hyperbolic equations of soliton type, previously proposed in the work of Habibullin et al. (2016 {\it J. Phys.…
We present a noncommutative generalization of Lax formalism of U(N) principal chiral model in terms of a one-parameter family of flat connections. The Lax formalism is further used to derive a set of parametric noncommutative B\"{a}cklund…
Let $\mathbb{G}(d,n)$ be the complex Grassmannian of affine $d$-planes in $n$-space. We study the problem of characterizing the set of algebraic subvarieties of $\mathbb{G}(d,n)$ invariant under the action of the maximal torus $T$ and…
A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of…
Inspired by the Bohlin transformation relating the planar harmonic oscillator to the Kepler problem, a variant of the Eisenhart lift is studied, in which a Lagrangian conservative dynamical system with d degrees of freedom is embedded into…
N-fold B\"acklund transformation for the Davey-Stewartson equation is constructed by using the analytic structure of the Lax eigenfunction in the complex eigenvalue plane. Explicit formulae can be obtained for a specified value of N. Lastly…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…
Two approaches to the study of cosmological density perturbations in modified theories of Palatini gravity have recently been discussed. These utilise, respectively, a generalisation of Birkhoff's theorem and a direct linearization of the…
To explain the recently reported large-scale spatial variations of the fine structure constant $\alpha$, we apply some models of curvature-nonlinear multidimensional gravity. Under the reasonable assumption of slow changes of all quantities…
We derive the conditions that the coupling constants of the Generalized Thirring Model have to satisfy in order for the model to admit an infinite number of commuting classical conserved quantities. Our treatment uses the bosonized version…
The perturbed NLS equation is asymptotically integrable if the zero-order approximation to the solution is a single soliton. It is not integrable for any other zero-order solution. In the standard application of a Normal Form expansion,…
Let G(d,n) denote the Grassmannian of d-planes in C^n and let T be the torus (C^*)^n/diag(C^*) which acts on G(d,n). Let x be a point of G(d,n) and let \bar{Tx} be the closure of the T-orbit through x. Then the class of the structure sheaf…
We present a new method to calculate formation of cosmological structure in the Newtonian limit. The method is based on Lagrangian perturbation theory plus two key theoretical extensions. One advance involves identifying and fixing a…
We prove the Bianchi permutability (existence of superposition principle) of B\"acklund transformations for asymmetric quad-equations. Such equations and there B\"acklund transformations form 3D consistent systems of a priori different…