Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · solv-int/9602001

Some Classes of Solutions to the Toda Lattice Hierarchy

Harold Widom
View original source ↗Read source document ↗Export metadata ↓

Abstract

We apply an analogue of the Zakharov-Shabat dressing method to obtain infinite matrix solutions to the Toda lattice hierarchy. Using an operator transformation we convert some of these into solutions in terms of integral operators and Fredholm determinants. Others are converted into a class of operator solutions to the $l$-periodic Toda hierarchy.

Explore related subjects

solv-inthep-thmath.FAnlin.SI

Keep this discovery

BibTeXRIS

Harold Widom. 1996-10-02. Some Classes of Solutions to the Toda Lattice Hierarchy. https://doi.org/10.1007/s002200050078

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2009

The tetrahedral analog of Veneziano amplitude

In solv-int/9812016 it was shown that the Veneziano amplitude in string theory comes naturally from one of the simplest solutions of the functional pentagon equation (FPE). More generally, FPE is intimately connected with the duality condition for scattering processes. Here I find the amplitude that comes the same way from a solution of the functional tetrahedron equation, with the duality replaced by the local Yang - Baxter equation.

solv-int↗
arXiv2004

Equations of Geodesic Deviation and the Inverse Scattering Transform

Solutions of equations of geodesic deviation in three- and four- dimensional spaces obtained by the inverse scattering transform are considered. It is shown that in the case of three-dimensional space solutions of geodesic deviation equations are reduced to solutions of the well-known Zakharov-Shabat problem. In four- dimensional space system of geodesic deviation equations is associated with $3\times 3$ matrix Schrödinger equation, and dependence on parameters defined by the nonlinear equations of three-wave interaction.

solv-int↗
arXiv2003

Polarization scattering by soliton-soliton collisions

Collision of two solitons of the Manakov system is analytically studied. Existence of a complete polarization mode switching regime is proved and the parameters of solitons prepared for polarization switching are found.

solv-int↗