Abstract
We outline several specific issues concerning the theory of multicomponent nonlinear Schrödinger equations with constant boundary conditions. We first study the spectral properties of the Lax operator L, the structure of the phase space \( \mathcal{M} \), and the construction of the fundamental analytic solutions. We then consider the regularized Wronskian relations, which allow analyzing the map between the potential of L and the scattering data. The Hamiltonian formulation also requires a regularization procedure.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 3, pp. 438–447, June, 2009.
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Gerdjikov, V.S., Kostov, N.A. & Valchev, T.I. Multicomponent nonlinear Schrödinger equations with constant boundary conditions. Theor Math Phys 159, 787–795 (2009). https://doi.org/10.1007/s11232-009-0067-6
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DOI: https://doi.org/10.1007/s11232-009-0067-6