Abstract
We prove that a dynamical system obtained by the space-time inversion of the nonlinear Schrödinger equation is equivalent to a generalized Dicke model. We study the complete Liouville integrability of the obtained dynamical system.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 126–128, January, 1995.
Thus, we have shown that the generalized Dicke model, inverse to the nonlinear Schrödinger equation, is a completely Liouville integrable Hamiltonian flow of hydrodynamic type.
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Samulyak, R.V. Generalized Dicke model as an integrable dynamical system inverse to the nonlinear Schrödinger equation. Ukr Math J 47, 149–151 (1995). https://doi.org/10.1007/BF01058807
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DOI: https://doi.org/10.1007/BF01058807