Decomposition Of A Class Of Nonlinear Equations And Their Quasi-periodic Solutions

Based on a new 3×3 eigenvalue problem, a new (1+1)-dimensional soliton hierarchy is presented. With the help of the nonlinearization approach of eigenvalue problems, a new finite-dimensional Hamiltonian system with a Lie-Poisson structure on the Poisson manifold R^3N is obtained. The Abel-Jacobi coordinates are introduced suitably to straighten out the Hamiltonian flows. Based on the decomposition and the theory of algebra curve, the explicit quasi-periodic solutions for the new (1+1)-dimensional equations are obtained.