4 research outputs found
Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations
A differential-algebraic approach to studying the Lax type integrability of
the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The
approach is also applied to studying the Lax type integrability of the well
known Korteweg-de Vries dynamical system.Comment: 11 page
Classical R-matrix theory for bi-Hamiltonian field systems
The R-matrix formalism for the construction of integrable systems with
infinitely many degrees of freedom is reviewed. Its application to Poisson,
noncommutative and loop algebras as well as central extension procedure are
presented. The theory is developed for (1+1)-dimensional case where the space
variable belongs either to R or to various discrete sets. Then, the extension
onto (2+1)-dimensional case is made, when the second space variable belongs to
R. The formalism presented contains many proofs and important details to make
it self-contained and complete. The general theory is applied to several
infinite dimensional Lie algebras in order to construct both dispersionless and
dispersive (soliton) integrable field systems.Comment: review article, 39 page
Riemann type algebraic structures and their differential-algebraic integrability analysis
The differential-algebraic approach to studying the Lax type integrability of generalized Riemann type equations is devised. The differentiations and the associated invariant differential ideals are analyzed in detail. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system