After recalling features of solitons in the Toda (more precisely an adapted Morse-Toda) lattice a succint discussion is provided about the stability of such solitons when the lattice is heated up to physiological temperatures for values of parameters typical of bio-macro-molecules. Then the discussion is focused on the soliton trapping of an added excess (originally free) electron thus creating...

In this paper we prove a sharp version of the Moser-Trudinger inequality for the Euler-Lagrange functional of a singular Toda system, motivated by the study of models in Chern-Simons theory. Our result extends those in [14] and [37] for the scalar case, as well as that in [23] for the regular Toda system. We expect this inequality to be a basic tool to attack variationally the existence problem...

We construct the classical W -algebras for some non-abelian Toda systems associated with the Lie groups GL 2n(R) and Spn(R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representaion for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements o...

A simple, basic, argument is given, based solely on energy-momentum considerations to recover conditions under which ar affine or conformal Toda field theories can support defects of integrable type. Associated triangle relations are solved to provide expressions for transmission matrices that generalize previously known examples calculated for the sine-Gordon model and the a2 affine Toda model...

Complexiton solutions (or complexitons for short) are exact solutions newly introduced to integrable equations. Starting with the solution classification for a linear differential equation, the Korteweg-de Vries equation and the Toda lattice equation are considered as examples to exhibit complexiton structures of nonlinear integrable equations. The crucial step in the solution process is to app...

We construct the classical W -algebras for some non-abelian Toda systems associated with the Lie groups GL 2n(R) and Spn(R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representaion for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements o...

We provide a brief review of the initial value problem associated with the Toda and Kac-van Moerbeke hierarchies. We give a simple proof for the basic (global) existence and uniqueness theorem and provide some additional details for the inverse scattering transform. In addition, we also show how to obtain solutions of the Kac-van Moerbeke hierarchy from solutions of the Toda hierarchy via a Miu...

The paper concerns the Hamiltonian structure of the finite-dimensional reductions 2D dispersionless Toda hierarchy constrained by the string equation. We derive the Hamiltonian structure of the reduced dynamics and show connections of integrals of “multi-finger” solutions of the Laplacian growth problem with the “Toda–Krichever” flows of the 2dToda hierarchy constrained by a string equation. Th...

Toda in his celebrated paper showed that the polynomial-time hierarchy is contained in P#P. We give a short and simple proof of the first half of Toda’s Theorem that the polynomial-time hierarchy is contained in BPP⊕P. Our proof uses easy consequences of relativizable proofs of results that predate Toda. For completeness we also include a proof of the second half of Toda’s Theorem. ACM Classifi...

We give a gauge invariant formulation of N = 2 supersymmetric abelian Toda field equations in N = 2 superspace. Superconformal invariance is studied. The conserved currents are shown to be associated with Drinfeld-Sokolov type gauges. The extension to non-abelian N = 2 Toda equations is discussed. Very similar methods are then applied to a matrix formulation in N = 2 superspace of one of the N ...