NONLINEARIZATION OF THE LAX SYSTEM FOR AKNS HIERARCHY
NONLINEARIZATION OF THE LAX SYSTEM FOR AKNS HIERARCHY
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发表时间：
1990
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通讯作者：
C. Cao
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作者：
C. Cao
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 + 1/2ψ1,ψ1ψ2,ψ2in 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((?)).
