Related papers: Symmetry properties of a nonlinear acoustics model
We deal with the problem of description of nonsingular pairs of compatible flat metrics for the general $N$-component case. We describe the scheme of the integrating the nonlinear equations describing nonsingular pairs of compatible flat…
We apply the SL(2,C) lattice Kac-Moody algebra of Alekseev, Faddeev and Semenov-Tian-Shansky to obtain a new lattice description of the SU(2) chiral model in two dimensions. The system has a global quantum group symmetry and it can be…
For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…
$k$-Para-K\"ahler Lie algebras are a generalization of para-K\"ahler Lie algebras $(k=1)$ and constitute a subclass of $k$-symplectic Lie algebras. In this paper, we show that the characterization of para-K\"ahler Lie algebras as left…
In this paper, we study a class of symmetry reduced models of $\mathcal{N}=1$ supergravity using self-dual variables. It is based on a particular Ansatz for the gravitino field as proposed by D'Eath et al. We show that the essential part of…
All coboundary Lie bialgebras and their corresponding Poisson--Lie structures are constructed for the oscillator algebra generated by $\{\aa,\ap,\am,\bb\}$. Quantum oscillator algebras are derived from these bialgebras by using the…
This paper is a contribution to the symmetry analysis of the gas dynamics system in the vein of the ''podmodeli'' (submodels) program outlined by Ovsyannikov (1994). We consider the case of the special state equation, prescribing pressure…
Certain features associated with the symmetry reduction of the vacuum Einstein equations by two commuting, space-like Killing vector fields are studied. In particular, the discussion encompasses the equations for the Gowdy $T^3$ cosmology…
We consider the symmetry algebra generated by the total angular momentum operators, appearing as constants of motion of the $\mathrm{S}_3$ Dunkl Dirac equation. The latter is a deformation of the Dirac equation by means of Dunkl operators,…
We define a new algebra, which can formally be considered as a ${\cal C}{\cal P}$ deformed $\mathfrak{su}(2)$ Lie algebra. Then, we present a one-dimensional quantum oscillator model, of which the wavefunctions of even and odd states are…
We generalize the Drinfeld-Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in…
The 1 + 2 dimensional Bogoyavlensky-Konopelchenko Equation is investigated for its solution and conservation laws using the Lie point symmetry analysis. In the recent past, certain work has been done describing the Lie point symmetries for…
We apply the theory of Lie symmetries in order to study a fourth-order $1+2$ evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries…
The objects under inspection, on a given probability space, are noise(-type) Boolean algebras -- distributive non-empty sublattices of the lattice of all complete sub-$\sigma$-fields, whose every element admits an independent complement.…
The generalized Drinfel'd-Sokolov hierarchies studied by de Groot-Hollowood-Miramontes are extended from the viewpoint of Sato-Wilson dressing method. In the A_1^(1) case, we obtain the hierarchy that include the derivative nonlinear…
By generalizing the Drinfeld-Sokolov reduction a large class of $W$ algebras can be constructed. We introduce 'finite' versions of these algebras by Poisson reducing Kirillov Poisson structures on simple Lie algebras. A closed and…
We process snapshots of trajectories of evolution equations with intrinsic symmetries, and demonstrate the use of recently developed eigenvector-based techniques to successfully quotient out the degrees of freedom associated with the…
We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential…
In this paper, we develop a method to obtain the algebraic classification of compatible pre-Lie algebras from the classification of pre-Lie algebras of the same dimension. We use this method to obtain the algebraic classification of complex…
This paper establishes a comprehensive algebraic framework linking the Lie algebra $\mathfrak{so}_{3}$ to the Askey--Wilson algebras. First, we provide a manifestly symmetric reformulation of the algebra homomorphism from the universal…