W–Gravity and Generalized Lax Equations for (super) Toda Theory

نویسنده

  • Kenichiro Aoki
چکیده

We generalize the Lax pair and Bäcklund transformations for Toda and N=1 super Toda equations to the case of arbitrary worldsheet background geometry. We use the fact that the Toda equations express constant curvature conditions, which arise naturally from flatness conditions equivalent to the W–gravity equations of motion.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

5 D ec 1 99 6 THE NONCRITICAL W ∞ STRING SECTOR OF THE MEMBRANE

The exact quantum integrability aspects of a sector of the membrane is investigated. It is found that spherical membranes (in the lightcone gauge) moving in flat target spacetime backgrounds admit a class of integrable solutions linked to SU (∞) SDYM equations (dimensionally reduced to one temporal dimension) which, in turn, are related to Plebanski 4D SD Gravitational equations. A further rota...

متن کامل

Integrable Discretisations for a Class of Nonlinear Schrödinger Equations on Grassmann Algebras

Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of thes...

متن کامل

A New Formulation of the Generalized Toda Lattice Equations and Their Fixed Point Analysis via the Momentum Map

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...

متن کامل

Higher Toda Mechanics and Spectral Curves

For each one of the Lie algebras gln and g̃ln, we constructed a family of integrable generalizations of the Toda chains characterized by two integers m+ and m−. The Lax matrices and the equations of motion are given explicitly, and the integrals of motion can be calculated in terms of the trace of powers of the Lax matrix L. For the case of m+ = m−, we find a symmetric reduction for each general...

متن کامل

Some new integrable equations from the self-dual Yang-Mills equations

Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are nonautonomous versions of the chiral model in (2 + 1) dimensions, generalized nonlinear Schrödinger, Korteweg-de Vries, Toda lattice, Garnier and Euler-Arnold equations. The Lax pairs for all of these equations are derived by the symmetry reductions of ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1992