A nonconfocal generator of involutive systems and three associated soliton hierarchies

Abstract

Quite a few new finite‐dimensional integrable systems have been obtained by the nonlinearization procedure of eigenvalue problems suggested by the author. Almost all of their associated involutive systems are generated from a confocal generator: Γ̂ k =∑ N j=1’(λ k −λ j )−1 B 2 k j , B k j =p k q j −p j q k . In the present paper, a nonconfocal generator Γ k =∑ N j=1’(λ2 k −λ2 j )−1 [(λ k −λ j )2 A 2 kj +ε(λ k +λ j )2 B 2 k j ], A k j =p k p j +εq k q j is found, from which some new integrable systems and soliton hierarchies are obtained.