Variational principle for the Zakharov-Shabat equations
نویسندگان
چکیده
منابع مشابه
Variational principle for Zakharov-Shabat equations in two-dimensions
We study the corresponding scattering problem for Zakharov and Shabat compatible differential equations in two-dimensions, the representation for a solution of the nonlinear Schrödinger equation is formulated as a variational problem in two-dimensions. We extend the derivation to the variational principle for the Zakharov and Shabat equations in one-dimension. We also developed an approximate a...
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In this article the scattering matrix pertaining to the defocusing matrix Zakharov-Shabat system on the line is related to the scattering operator arising from time-dependent scattering theory. Further, the scattering data allowing for a unique retrieval of the potential in the defocusing matrix Zakharov-Shabat system are characterized. Mathematics Subject Classification (2000). Primary 34A55, ...
متن کاملEstimates for periodic Zakharov-Shabat operators
We consider the periodic Zakharov-Shabat operators on the real line. The spectrum of this operator consists of intervals separated by gaps with the lengths |gn| > 0, n ∈ Z. Let μn be the corresponding effective masses and let hn be heights of the corresponding slits in the quasimomentum domain. We obtain a priori estimates of sequences g = (|gn|)n∈Z, μ± = (μn )n∈Z, h = (hn)n∈Z in terms of weigh...
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The dressing procedure for the Generalised Zakharov-Shabat system is well known for systems, related to sl(N) algebras. We extend the method, constructing explicitly the dressing factors for some systems, related to orthogonal and symplectic Lie algebras. We consider ’dressed’ fundamental analytical solutions with simple poles at the prescribed eigenvalue points and obtain the corresponding Lax...
متن کاملWave operators for the matrix Zakharov–Shabat system
In this article, we prove the similarity and, in the focusing case, the J-unitary equivalence of the free Hamiltonian and the restriction of the full Hamiltonian to the maximal invariant subspace on which its spectrum is real for the matrix Zakharov–Shabat system under suitable conditions on the potentials. This restriction of the full Hamiltonian is shown to be a scalar-type spectral operator ...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 1995
ISSN: 0167-2789
DOI: 10.1016/0167-2789(95)00057-b