ISSN:
1089-7658
Quelle:
AIP Digital Archive
Thema:
Mathematik
,
Physik
Notizen:
An eigenvalue problem and the associated hierarchy of nonlinear soliton equations are proposed in this paper. In particular, a representative system of generalized AKNS soliton equations in the hierarchy is given, namely, qt=−〈fraction SHAPE="CASE"〉12 qxx+q2r−2μq2rx−2μrqqx+2μ2q3r2, rt=〈fraction SHAPE="CASE"〉12 rxx−qr2−2μr2qx−2μqrrx+2μ2q2r3. N-Hamiltonian structures are also established for all the hirarchy of generalized AKNS soliton equations based on N+1 pairs of Hamiltonian pairs. And then the eigenvalue problem is nonlinear as a finite-dimensional completely integrable Hamiltonian system under the Bargmann constraint between the potentials and the eigenvalue functions, and its involutive system is also given. Finally, the involutive solutions of the hierarchy of generalized AKNS soliton equations are found, in particular, the involutive solutions of the system of generalized Schrödinger equations are given. © 2001 American Institute of Physics.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1063/1.1289379
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