From dispersionless to soliton systems via Weyl-Moyal like deformations

Abstract

The formalism of quantization deformation is reviewed and the Weyl-Moyal like deformation is applied to systematic construction of the field and lattice integrable soliton systems from Poisson algebras of dispersionless systems.

26 pages

References in corpus (3)

• Classical R-matrix theory of dispersionless systems: I. (1+1)-dimension theory
• Classical $\mathbf{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras
• Conformal Covariantization of Moyal-Lax Operators

Cited by in corpus (10)

• Classical R-matrix theory for bi-Hamiltonian field systems
• Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems
• S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies
• Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems
• On the r-th dispersionless Toda hierarchy I: Factorization problem, symmetries and some solutions
• Dispersionful analogue of the Whitham hierarchy
• Integrable discrete systems on R and related dispersionless systems
• A new approach to deformation equations of noncommutative KP hierarchies
• Gauge transformation and reciprocal link for (2+1)-dimensional integrable field systems
• On deformations of standard R-matrices for integrable infinite-dimensional systems