相关论文: Symmetries of Toda Equations
An approach to master symmetries of lattice equations is proposed by the use of discrete zero curvature equation. Its key is to generate non-isospectral flows from the discrete spectral problem associated with a given lattice equation. A…
A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The…
In the present paper the non-Noether symmetries of the Toda model, nonlinear Schodinger equation and Korteweg-de Vries equations (KdV and mKdV) are discussed. It appears that these symmetries yield the complete sets of conservation laws in…
A class of exact solutions of the dispersionless Toda hierarchy constrained by a string equation is obtained. These solutions represent deformations of analytic curves with a finite number of nonzero harmonic moments. The corresponding…
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…
We use coherent states as a time-dependent variational ansatz for a semiclassical treatment of the dynamics of anharmonic quantum oscillators. In this approach the square variance of the Hamiltonian within coherent states is of particular…
In this paper, we construct a new even constrained B(C) type Toda hierarchy and derive its B(C) type Block type additional symmetry. Also we generalize the B(C) type Toda hierarchy to the $N$-component B(C) type Toda hierarchy which is…
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
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…
In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…
The study of symmetries of partial differential equations (PDEs) has been traditionally treated as a geometrical problem. Although geometrical methods have been proven effective with regard to finding infinitesimal symmetry transformations,…
The generators and commutation relations are calculated explicitly for higher symmetry algebras of a class of hyperbolic Euler-Lagrange systems of Liouville type (in particular, for 2D Toda chains associated with semi-simple complex Lie…
We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…
The equation of motion of affine Toda field theory is a coupled equation for $r$ fields, $r$ is the rank of the underlying Lie algebra. Most of the theories admit reduction, in which the equation is satisfied by fewer than $r$ fields. The…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used…
This paper deals with the dynamics of time-reversible Hamiltonian vector fields with 2 and 3 degrees of freedom around an elliptic equilibrium point in presence of symplectic involutions. The main results discuss the existence of…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
We give an explicit formula for the solution to the initial value problem of the full symmetric Toda hierarchy. The formula is obtained by the orthogonalization procedure of Szeg\"{o}, and is also interpreted as a consequence of the QR…
Group classification of classes of mKdV-like equations with time-dependent coefficients is carried out. The usage of equivalence transformations appears a crucial point for the exhaustive solution of the problem. We prove that all the…