Based on the nonlinearization of Lax pairs, the Korteweg-de Vries (KdV) soliton hierarchy is decomposed into a family of finite-dimensional Hamiltonian systems, whose Liouville integrability is proved by means of th...Based on the nonlinearization of Lax pairs, the Korteweg-de Vries (KdV) soliton hierarchy is decomposed into a family of finite-dimensional Hamiltonian systems, whose Liouville integrability is proved by means of the elliptic coordinates. By applying the Abel-Jacobi coordinates on a Riemann surface of hyperelliptic curve, the resulting Hamiltonian flows as well as the KdV soliton hierarchy are ultimately reduced into linear superpositions, expressed by the Abel-Jacobi variables.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10471132 and the Special Foundation for.the State Key Basic Research Project "Nonlinear Science"
文摘Based on the nonlinearization of Lax pairs, the Korteweg-de Vries (KdV) soliton hierarchy is decomposed into a family of finite-dimensional Hamiltonian systems, whose Liouville integrability is proved by means of the elliptic coordinates. By applying the Abel-Jacobi coordinates on a Riemann surface of hyperelliptic curve, the resulting Hamiltonian flows as well as the KdV soliton hierarchy are ultimately reduced into linear superpositions, expressed by the Abel-Jacobi variables.