Related papers: Nonlocal symmetries of integrable two-field diverg…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
We summarize our work on "hidden" Noether symmetries of multifield cosmological models and the classification of those two-field cosmological models which admit such symmetries.
We discuss geometric properties of non-Noether symmetries and their possible applications in integrable Hamiltonian systems. Correspondence between non-Noether symmetries and conservation laws is revisited. It is shown that in regular…
We generalize earlier results of Fokas and Liu and find all locally analytic (1+1)-dimensional evolution equations of order $n$ that admit an $N$-shock type solution with $N\leq n+1$. To this end we develop a refinement of the technique…
The models of the non-linear optics in which solitons were appeared are considered. These models are of paramount importance in studies of non-linear wave phenomena. The classical examples of phenomena of this kind are the self-focusing,…
We give a natural notion of nondegeneracy for singular points of integrable non-Hamiltonian systems, and show that such nondegenerate singularities are locally geometrically linearizable and deformation rigid in the analytic case. We…
Recently it has been discovered that some nonlinear evolution equations in 2+1 dimensions, which are integrable by the use of the Spectral Transform, admit localized (in the space) soliton solutions. This article briefly reviews some of the…
An infinite sequence of commuting nonpolynomial contact symmetries of the two-dimensional minimal surface equation is constructed. Local and nonlocal conservation laws for $n$-dimensional minimal area surface equation are obtained by using…
We construct examples of non-invertible global symmetries in two-dimensional superconformal field theories described by sigma models into Calabi-Yau target spaces. Our construction provides some of the first examples of non-invertible…
Motion of curves and surfaces in $\R^3$ lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through…
An exactly solvable model for the multi-level system interacting with several reservoirs at zero temperatures is presented. Population decay rates and decoherence rates predicted by exact solution and several approximate master equations,…
We determine hidden conformal symmetries behind the evolution equations of black hole perturbations in a vector-tensor theory of gravity. Such hidden symmetries are valid everywhere in the exterior region of a spherically symmetric,…
We associate an square to any two dimensional evolution algebra. This geometric object is uniquely determined, does not depend on the basis and describes the structure and the behaviour of the algebra. We determine the identities of degrees…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal…
We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in three tightly inter-related domains: the variational Poisson…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is indeed possible to understand the nonlinear clustering in terms of three well defined regimes:…
We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the non-commutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the…
It is shown that each integrable mapping is connected with a hierarchical completely integrable sytem of equations of evolution type which are invariant with respect to the transformation described by this mapping.
We investigate the nonequilibrium evolution of a scalar field in (2+1) dimensions. The field is set in a double-well potential in contact (open) or not (closed) with a heat bath. For closed systems, we observe the synchronized emergence of…