The Moyal bracket and the dispersionless limit of the KP hierarchy

Abstract

A new Lax equation is introduced for the KP hierarchy which avoids the use of pseudo-differential operators, as used in the Sato approach. This Lax equation is closer to that used in the study of the dispersionless KP hierarchy, and is obtained by replacing the Poisson bracket with the Moyal bracket. The dispersionless limit, underwhich the Moyal bracket collapses to the Poisson bracket, is particularly simple.

9 pages, LaTeX

References in corpus (4)

• A One-Parameter Family of Hamiltonian Structures for the KP Hierarchy and a Continuous Deformation of the Nonlinear $\W_{\rm KP}$ Algebra
• Dressing operator approach to Moyal algebraic deformation of selfdual gravity
• Nonabelian KP hierarchy with Moyal algebraic coefficients
• Large Nonlinear $W_{\infty }$ Algebras from Nonlinear Integrable Deformations of Self Dual Gravity

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• Conformal Covariantization of Moyal-Lax Operators
• Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems