arXiv subjects

Cestmir Burdik

Publications and source records attributed to Cestmir Burdik.

5 recordsLinked to original sources

arXiv2019

Soliton solutions and traveling wave solutions for the two-dimensional generalized nonlinear Schrödinger equations

In this paper, we present the two-dimensional generalized nonlinear Schrödinger equations with the Lax pair. These equations are related to many physical phenomena in the Bose-Einstein condensates, surface waves in deep water and nonlinear optics. The existence of the Lax pair defines integrability for the partial differential equation, so the two-dimensional generalized nonlinear Schrödinger equations are integrable. We obtain bilinear forms of the two-dimensional GNLS equations. One- and two-soliton solutions are derived via the Hirota bilinear method, a procedure quite useful in the solution of nonlinear partial differential equations. We apply the extended tanh method in order to construct new exact traveling wave solutions. Through 3D plots, we show the dynamical behavior of the obtained solutions.

nlin.SI↗

arXiv2017

Nested Bethe ansatz for RTT--algebra of sp(4) type

We study the highest weight representations of the RTT--algebras for the R--matrix sp(4) type by the nested algebraic Bethe ansatz. These models were solved by Reshetikhin for sp(2n) but using a very special type of representation. The explicit construction of the Bethe vectors is carried out in the general case and the explicit formulae for the Bethe equations are derived. In conclusion, the direct generalization for sp(2n) is formulated.

math-ph↗

arXiv2011

On representations of Higher Spin symmetry algebras for mixed-symmetry HS fields on AdS-spaces. Lagrangian formulation

We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux $Y(s_1,...,s_k)$ with $k\geq 2$ rows on $d$-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for $k=2$ Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic $sp(2k)$ algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin $(s_1,s_2)$ is derived.

hep-th↗

arXiv2009

Remarks on Multi-Dimensional Conformal Mechanics

Recently, Galajinsky, Lechtenfeld and Polovnikov proposed an elegant group-theoretical transformation of the generic conformal-invariant mechanics to the free one. Considering the classical counterpart of this transformation, we relate this transformation with the Weil model of Lobachewsky space.

math-ph↗

arXiv2003

Bernuau spline wavelets and Sturmian sequences

A spline wavelets construction of class C^n(R) supported by sequences of aperiodic discretizations of R is presented. The construction is based on multiresolution analysis recently elaborated by G. Bernuau. At a given scale, we consider discretizations that are sets of left-hand ends of tiles in a self-similar tiling of the real line with finite local complexity. Corresponding tilings are determined by two-letter Sturmian substitution sequences. We illustrate the construction with examples having quadratic Pisot-Vijayaraghavan units (like tau = (1 + sqrt{5})/2 or tau^2 = (3 + sqrt{5})/2) as scaling factor. In particular, we present a comprehensive analysis of the Fibonacci chain and give the analytic form of related scaling functions and wavelets as splines of second order. We also give some hints for the construction of multidimensional spline wavelets based on stone-inflation tilings in arbitrary dimension.

math-ph↗