(1 +1)-dimensional (2 +1)-dimensional Soliton Equations Decomposition And Its Quasi-periodic Solutions

In this paper, a new spectral problem is proposed,and nonlinear differential equations of the corresponding hierarchy are obtained. With the help of the nonlinearization approach of eigenvalue problems, a new finite-dimensional Hamiltonian system on R²ⁿ is obtained. A generating function approach is introduced to prove the involutivity of conserved integrals and its functional independence, and the Hamiltonian flows are straightened by introducing the Abel-Jacobi coordinates. At last, based on the principles of algebrac curve, the quasi-periodic solutions for the stationary equations (4.2) and the (1+1)-dimentional soliton equations (1.13) (1.14) and (2+1)-dimentional soliton equation (1.20) are obtaited by solving the ordinary differential equations and inversing the Abel-Jacobi coordinates.