We study the following generalized SU(3) Toda System

We consider the following Toda system

We study the ultraviolet asymptotics in aane Toda theories. These models are considered as perturbed non-aane Toda theories. We calculate the reeection amplitudes, which relate diierent exponential elds with the same quantum numbers. Using these amplitudes we derive the quantization condition for the vacuum wave function, describing zero-mode dynamics, and calculate the UV asymptotics of the ee...

We give a simple proof that the Neumann coefficients of surface states in Witten’s SFT satisfy the Hirota equations for dispersionless KP hierarchy. In a similar way we show that the Neumann coefficients for the three string vertex in the same theory obey the Hirota equations of the dispersionless Toda Lattice hierarchy. We conjecture that the full (dispersive) Toda Lattice hierachy and, even m...

We study the ultraviolet asymptotics in affine Toda theories. These models are considered as perturbed non-affine Toda theories. We calculate the reflection amplitudes, which relate different exponential fields with the same quantum numbers. Using these amplitudes we derive the quantization condition for the vacuum wave function, describing zero-mode dynamics, and calculate the UV asymptotics o...

with b0 = bn = 0. The Toda lattice is an integrable system that is solved explicitly by the inverse spectral method (see [M]). Deift and McLaughlin [DM] studied the continuum limit of the Toda lattice. Here the size n tends to infinity, and we write ak(t;n) and bk(t;n) to indicate the dependence on n. For given continuous functions a0(y) and b0(y) > 0 for y ∈ (0,1), Deift and McLaughlin [DM] ta...

We find soliton-like solutions in a particular case of non-abelian loop Toda equations associated with general linear groups. We use the formalism of rational dressing based on appropriate block-matrix representation suggested by the Z-gradation under consideration. We present solutions in a form of a direct matrix generalization of the Hirota’s soliton constructions already well-known for the ...

We prove that the extended Toda hierarchy of [1] admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators Lm, m ≥ −1 of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination...

Orbital and asymptotic stability for 1-soliton solutions to the Toda lattice equations as well as small solitary waves to the FPU lattice equations are established in the energy space. Unlike analogous Hamiltonian PDEs, the lattice equations do not conserve momentum. Furthermore, the Toda lattice equation is a bidirectional model that does not fit in with existing theory for Hamiltonian system ...

The low energy effective actions which arise from string theory or M-theory are considered in the cosmological context, where the graviton, dilaton and antisymmetric tensor field strengths depend only on time. We show that previous results can be extended to include cosmological solutions that are related to the EN Toda equations. The solutions of the Wheeler-DeWitt equation in minisuperspace a...