Related papers: Generalized conditional symmetries of evolution eq…
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further…
The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the…
The continuous dependence of solutions to certain (non-autonomous, partial, integro-differential-algebraic, evolutionary) equations on the coefficients is addressed. We give criteria that guarantee that convergence of the coefficients in…
Q-conditional symmetries of the classical Lotka-Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is constructed. The relevant non-Lie ans\"atze to reduce the classical…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…
Variational and divergence symmetries are studied in this paper for linear equations of maximal symmetry in canonical form, and the associated first integrals are given in explicit form. All the main results obtained are formulated as…
Theoretical studies on evolutionary algorithms have developed vigorously in recent years. Many such algorithms have theoretical guarantees in both running time and approximation ratio. Some approximation mechanism seems to be inherently…
In population games, a large population of players, modeled as a continuum, is divided into subpopulations, and the fitness or payoff of each subpopulation depends on the overall population composition. Evolutionary dynamics describe how…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a…
Symmetry, which describes invariance, is an eternal concern in mathematics and physics, especially in the investigation of solutions to the partial differential equation (PDE). A PDE's nonlocally related PDE systems provide excellent…
We study the symmetry reduction of nonlinear evolution and wave type differential equations by using operators of non-point symmetry. In our approach we use both operators of classical and conditional symmetry. It appears that the…
The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invarint solution for it are obtained by means of this technique. Polynomial, trigonometric and elliptic function solutions can be…
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…
The concept of evolutionarily stability and its relation with the fixed points of the replicator equation are important aspects of evolutionary game dynamics. In the light of the fact that oscillating state of a population and individuals…
We provide a complete classification of generalized and formal symmetries and local conservation laws for an evolution equation which generalizes the Kawahara equation having important applications in the study of plasma waves and…
Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
A one-parameter generalization of the hierarchy of negative flows is introduced for integrable hierarchies of evolution equations, which yields a wider (new) class of non-evolutionary integrable nonlinear wave equations. As main results,…