Abstract
A hierarchy of new nonlinear evolution equations is proposed, which are composed of the positive and negative coupled KdV flows. Based on the theory of algebraic curve, the corresponding flows are straightened under the Abel-Jacobi coordinates. The meromorphic function ϕ, the Baker-Akhiezer vector , and the hyperelliptic curve are introduced by which quasi-periodic solutions of the first two nonlinear evolution equations in the hierarchy are constructed according to the asymptotic properties and the algebro-geometric characters of ϕ, and
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