One of the well-known convergence acceleration methods, the ε-algorithm is investigated from the viewpoint of the Toda molecule equation. It is shown that the error caused by the algorithm is evaluated by means of solutions for the equation. The acceleration algorithm based on the discrete Toda molecule equation is also presented. Discrete integrable systems play important roles in the field of...

A N = 4 supersymmetric matrix KP hierarchy is proposed and a wide class of its reductions which are characterized by a finite number of fields are described. This class includes the one-dimensional reduction of the two-dimensional N = (2|2) superconformal Toda lattice hierarchy possessing the N = 4 supersymmetry – the N = 4 Toda chain hierarchy – which may be relevant in the construction of sup...

A N = 4 supersymmetric matrix KP hierarchy is proposed and a wide class of its reductions which are characterized by a finite number of fields are described. This class includes the one-dimensional reduction of the two-dimensional N = (2|2) superconformal Toda lattice hierarchy possessing the N = 4 supersymmetry – the N = 4 Toda chain hierarchy – which may be relevant in the construction of sup...

One of the well-known convergence acceleration methods, the ε-algorithm is investigated from the viewpoint of the Toda molecule equation. It is shown that the error caused by the algorithm is evaluated by means of solutions for the equation. The acceleration algorithm based on the discrete Toda molecule equation is also presented. Discrete integrable systems play important roles in the field of...

The Toda flows are examples of integrable Hamiltonian systems which are of great interest from the point of view of pure mathematics as well as in applications. They originated as a description of a 1-dimensional lattice of particles with exponential interaction [29]. Flaschka [14] found a Lax pair for the equations and Moser [25] analyzed the dynamics and scattering behavior of the system. Adl...

This operator is a quantization of the Hamiltonian of the Toda lattice on n+1 identical particles with configuration coordinates t0, ..., tn and with the exponential interaction potential exp(ti−ti−1) of neighbors. The Toda lattice is known to be integrable on both classical and quantum levels: there exist commuting differential polynomials Dm(~∂/∂t, exp t, ~), m = 0, ..., n, which play the rol...

This operator is a quantization of the Hamiltonian of the Toda lattice on n+1 identical particles with configuration coordinates t0, ..., tn and with the exponential interaction potential exp(ti−ti−1) of neighbors. The Toda lattice is known to be integrable on both classical and quantum levels: there exist commuting differential polynomials Dm(~∂/∂t, exp t, ~), m = 0, ..., n, which play the rol...

Anharmonic interactions in lattices may sustain robust oscillatory modes and (nonlinear) waves including solitons. This is illustrated here by using an exponentially repulsive interaction introduced by Toda. To cope with friction and dissipation -always present in real systemsand hence to make robust, e.g., solitons, following Lord Rayleigh, an appropriate input-output energy balance is added t...

Abstract. The Pfaff lattice is an integrable system arising from the SR-group factorization in an analogous way to how the Toda lattice arises from the QR-group factorization. In our recent paper [Intern. Math. Res. Notices, (2007) rnm120], we studied the Pfaff lattice hierarchy for the case where the Lax matrix is defined to be a lower Hessenberg matrix. In this paper we deal with the case of ...

We restrict affine Toda field theory to the half-line by imposing certain boundary conditions at x = 0. The resulting theory possesses the same spectrum of solitons and breathers as affine Toda theory on the whole line. The classical solutions describing the reflection of these particles off the boundary are obtained from those on the whole line by a kind of method of mirror images. Depending o...