相关论文: Time Dependent Recursion Operators and Symmetries
We analyze the relationship of generalized conditional symmetries of evolution equations to the formal compatibility and passivity of systems of differential equations as well as to systems of vector fields in involution. Earlier results on…
We derive the general conditions for fully-nonlinear symmetry-integrable second-order evolution equations and their first-order recursion operators. We then apply the established Propositions to find links between a class of fully-nonlinear…
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…
In this paper we give definitions of basic concepts such as symmetries, first integrals, Hamiltonian and recursion operators suitable for ordinary differential equations on associative algebras, and in particular for matrix differential…
The recursion operators admitted by different operator Burgers equations, in the framework of the study of nonlinear evolution equations, are here con- sidered. Specifically, evolution equations wherein the unknown is an operator acting on…
We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the…
$\mathcal{PT}$ symmetry, that is, a combined parity and time-reversal symmetry is a key milestone for non-Hermite systems exhibiting entirely real eigenenergy. In the present work, motivated by a recent experiment, we study $\mathcal{PT}$…
We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms…
We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spaces in Cartan's classification and having additional…
We present an outline of a technique to associate certain methods from time optimal quantum control with various transforms on SU(3). Unitary operators are taken from certain time dependent Hamiltonians and transformation laws are derived.…
Prior work on computable defect-based local error estimators for (linear) time-reversible integrators is extended to nonlinear and nonautonomous evolution equations. We prove that the asymptotic results from the linear case [W. Auzinger and…
The evolution equations mentioned in the title of this paper read as follows: x~n = P(n)(x1; x2) , n = 1, 2 , where l is the "discrete-time" independent variable taking integer values (l =0, 1, 2, ...), xn = xn (l) are the 2 dependent…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
A geometrical formulation for adjoint-symmetries as 1-forms is studied for general partial differential equations (PDEs), which provides a dual counterpart of the geometrical meaning of symmetries as tangent vector fields on the solution…
In our article "A tree of linearisable second-order evolution equations by generalised hodograph transformations" [J. Nonlin. Math. Phys. {\bf 8} (2001), 342-362] we presented a tree of linearisable (C-integrable) second-order evolution…
Time reversal symmetry occupies a distinctive role in quantum mechanics, fundamentally requiring an anti-unitary operator to ensure a physically consistent representation. As such, the time reversal operator combines a unitary…
Direct and inverse recursion operator is derived for the vacuum Einstein equations for metrics with two commuting Killing vectors that are orthogonal to a foliation by 2-dimensional leaves.
The evolution, as functions of the "ticking time" $\ell =0,1,2,...$, of the solutions of the system of $N$ quadratic recursions \begin{eqnarray*} x_{n}\left( \ell +1\right) =c_{n}+\sum_{m=1}^{N}\left[ C_{nm}x_{m}\left( \ell \right) \right]…
The evolution of any factorized time-reversible symplectic integrators, when applied to the harmonic oscillator, can be exactly solved in a closed form. The resulting modified Hamiltonians demonstrate the convergence of the Lie series…
The time evolution of the correlation functions of an ensemble of anharmonic N-component oscillators with O(N) symmetry is described by a flow equation, exact up to corrections of order $1/N^2$. We find effective irreversibility.…