Lax matrix and a generalized coupled KdV hierarchy

Based on the study of the confocal Lax matrix, new confocal involutive systems and a new spectral problem are proposed from which a hierarchy of generalized coupled KdV equations is derived. The Abel–Jacobi coordinates are introduced to straighten out the associated flows. Algebro-geometric solutions of the generalized coupled KdV soliton equations are obtained with the help of Jacobi inversion. A generating function approach is used to prove the involutivity and the functional independence of the conserved integrals.