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Integration of the nonlinear Schroedinger equation with a self-consistent source

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Abstract

It is shown that the nonlinear Schroedinger equation with a self-consistent source admits investigation by the inverse scattering method for the Dirac operator. The conditions are found under which the solutions of the nonlinear Schroedinger equation with a self-consistent source describe the creation and annihilation of solitons.

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References

  1. Zakharov, V.E., Shabat, A.B.: Exact theory of two-dimensional self-focussing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP34, 62 (1972)

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  2. Mel'nikov, V.K.: JINR Preprint P2-88-668, Dubna 1988

  3. Mel'nikov, V.K.: JINR Preprint P2-88-728, Dubna 1988

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Authors and Affiliations

  1. Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Head Post Office, P.O. Box 79, SU-101000, Moscow, USSR

    V. K. Mel'nikov

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  1. V. K. Mel'nikov
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Communicated by H. Araki

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Mel'nikov, V.K. Integration of the nonlinear Schroedinger equation with a self-consistent source. Commun.Math. Phys. 137, 359–381 (1991). https://doi.org/10.1007/BF02431884

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  • DOI: https://doi.org/10.1007/BF02431884

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