A nonconfocal generator of involutive systems and three associated soliton hierarchies

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: Γk =∑Nj=1’(λk−λj)−1 B2kj, Bkj =pkqj −pjqk. In the present paper, a nonconfocal generator Γk =∑Nj=1’(λ2k−λ2j)−1 [(λk−λj)2A2kj+e(λk+λj)2 B2kj], Akj =pkpj +eqkqj is found, from which some new integrable systems and soliton hierarchies are obtained.