The Lax system for the AKNS vector field is nonlinearized and becomes naturally compatible under the constraint induced by a relation (q,r) = f(ψ) between reflectionless potentials and the eigenfunctions of the Zakha...The Lax system for the AKNS vector field is nonlinearized and becomes naturally compatible under the constraint induced by a relation (q,r) = f(ψ) between reflectionless potentials and the eigenfunctions of the Zakharov-Shabat eigenvalue problem (ZS). The spatial part (ZS) is nonlinearized as a completely integrable system in the Liouville sense with the Hamiltonian:H = <iZψ1, ψ2> + 1/2<ψ1,ψ1><ψ2,ψ2>in the symplectic manifold (R2N, dψ1(?)dψ2), whose solution variety (?) is an invariant set of the S-flow defined by the nonlinearized time part. Moreover, f maps (?) into the solution variety of a stationary AKNS equation, and maps the S-flow on (?) into the AKNS-flow on f((?)).展开更多
基金Project supported by the National Natural Science Foundation of China
文摘The Lax system for the AKNS vector field is nonlinearized and becomes naturally compatible under the constraint induced by a relation (q,r) = f(ψ) between reflectionless potentials and the eigenfunctions of the Zakharov-Shabat eigenvalue problem (ZS). The spatial part (ZS) is nonlinearized as a completely integrable system in the Liouville sense with the Hamiltonian:H = <iZψ1, ψ2> + 1/2<ψ1,ψ1><ψ2,ψ2>in the symplectic manifold (R2N, dψ1(?)dψ2), whose solution variety (?) is an invariant set of the S-flow defined by the nonlinearized time part. Moreover, f maps (?) into the solution variety of a stationary AKNS equation, and maps the S-flow on (?) into the AKNS-flow on f((?)).
