Related papers: Group-invariant solutions of a nonlinear acoustics…
Soliton solutions are recovered as scale-invariant asymptotic states of vacuum inhomogeneous cosmologies using renormalization group method. The stability analysis of these states is also given.
We present a new technique for constructing solutions of quasilinear systems of first-order partial differential equations, in particular inhomogeneous ones. A generalization of the Riemann invariants method to the case of inhomogeneous…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
We consider an inhomogeneous quantum supergroup which leaves invariant a supersymmetric particle algebra. The quantum sub-supergroups of this inhomogeneous quantum supergroup are investigated.
We develop a new connection between Differential Algebra and Geometric Invariant Theory, based on an anti-equivalence of categories between solution algebras associated to a linear differential equation (i.e. differential algebras generated…
Two different sets of collective-coordinate equations for solitary solutions of Nonlinear Klein-Gordon (NKG) model is introduced. The collective-coordinate equations are derived using different approaches for adding the inhomogeneities as…
The mixed problem for the implicit degenerating nonlinear parabolic equation is considered, and the solvability and behavior of solutions of this problem are studied. Furthermore, some classes of function spaces and their relations with…
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…
In this paper, a complete Lie symmetry analysis of the damped wave equation with time-dependent coefficients is investigated. Then the invariant solutions and the exact solutions generated from the symmetries are presented. Moreover, a Lie…
A class of negative order Ablowitz--Kaup--Newell--Segur nonlinear evolution equations are obtained by applying the Lax hierarchy of the first order linear system of three equations. The inverse scattering problem on the whole axis are…
Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of…
We extend unbounded Kasparov theory to encompass conformal group and quantum group equivariance. This new framework allows us to treat conformal actions on both manifolds and noncommutative spaces. As examples, we present unbounded…
We find extremely general classes of nonsmooth open sets which guarantee Mosco convergence for corresponding Sobolev spaces and the validity of Sobolev inequalities with a uniform constant. An important feature of our results is that the…
We present a notion of symmetry for 1+1-dimensional integrable systems which is consistent with their group theoretic description and reproduces in special cases the known Baecklund transformation for the generalized Korteweg-deVries…
It is known that solutions of the Knizhnik-Zamolodchikov differential equations are given by integrals of closed differential forms over suitable cycles. In this paper a quantization of this geometric construction is described leading to…
We study the application of generalized symmetry for reducing nonlinear partial differential equations. We construct the ansatzes for dependent variable $u$ which reduce the scalar partial differential equation with two independent…
We propose two types of stochastic extensions of nonholonomic constraints for mechanical systems. Our approach relies on a stochastic extension of the Lagrange-d'Alembert framework. We consider in details the case of invariant nonholonomic…
We provide new regularity results for the solutions of the Kolmogorov equation associated to a SPDE with nonlinear diffusion coefficients and a Burgers type nonlinearity. This generalizes previous results in the simpler cases of additive or…
A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group…
We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…