论文信息 - The finite-band solution of the Jaulent–Miodek equation

The finite-band solution of the Jaulent–Miodek equation

A method to construct the finite-band solution to the soliton equation is presented. We take the Jaulent–Miodek equation as an example. With the use of the nonlinearization of Lax pair, the Jaulent–Miodek equation is decomposed into two finite-dimensional integrable systems, whose properties are studied from the view of an r-matrix. Then through solving these finite-dimensional integrable systems, the finite-band solution of the Jaulent–Miodek equation is obtained.

Ruguang Zhou | Ruguang Zhou

[1] H. H. Chen,et al. Study of quasiperiodic solutions of the nonlinear Schrödinger equation and the nonlinear modulational instability , 1984 .

[2] S. Novikov,et al. Theory of Solitons: The Inverse Scattering Method , 1984 .

[3] M. Ablowitz,et al. The Periodic Cubic Schrõdinger Equation , 1981 .

[4] Leon A. Takhtajan,et al. Hamiltonian methods in the theory of solitons , 1987 .

[5] E. Sklyanin,et al. Separation of variables , 2004, Mathematical Methods of Theoretical Physics.

[6] Marcel Jaulent,et al. Nonlinear evolution equations associated with ‘enegry-dependent Schrödinger potentials’ , 1976 .

[7] Classical and quantum integrable systems in 263-1263-1263-1and separation of variables , 1993, hep-th/9312035.

[8] Separation of variables in the classical integrableSL(3) magnetic chain , 1992, hep-th/9211126.

[9] Separation of variables for the classical and quantum Neumann model , 1992, hep-th/9201035.

[10] Yunbo Zeng,et al. The deduction of the Lax representation for constrained flows from the adjoint representation , 1993 .

[11] S. Rauch-Wojciechowski,et al. Constrained flows of integrable PDEs and bi-Hamiltonian structure of the Garnier system , 1990 .

[12] Joe W. Harris,et al. Principles of Algebraic Geometry , 1978 .

[13] M. Jaulent. Inverse scattering problems in absorbing media , 1976 .

[14] O. Babelon,et al. Hamiltonian structures and Lax equations , 1990 .