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N-Soliton Interactions for the Manakov System: Effects of External Potentials

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Localized Excitations in Nonlinear Complex Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 7))

Abstract

We analyze the dynamical behavior of the N-soliton train in adiabatic approximation of the Manakov system (MS) perturbed by three types of external potentials: periodic, quadratic and quartic ones. We show that the dynamics of the N-soliton train is modeled by a perturbed complex Toda chain for certain choices of the train parameters and for small magnitudes of the intensities of the potentials. Possible applications of these results for Bose-Einstein condensates are discussed.

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Acknowledgements

This paper is dedicated to the late Professor Evgeni Doktorov with whom this topic was started. One of us (V.S.G.) is grateful also to Professor Jesus Cuevas Maraver and to the Organizing Committee of LENCOS-2 for the chance to participate in the conference. We are obliged to Professor Anca Visinescu and Dr. Assen Kyuldjiev for useful discussions and help, Finally, we thank the anonymous referees for careful reading of the manuscript.

This work is supported in part by the National Science Foundation of the Bulgarian Ministry of Youth, Education and Science under grant DDVU02/71.

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Authors and Affiliations

  1. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, Blvd., 1784, Sofia, Bulgaria

    V. S. Gerdjikov

  2. Department of Applied Mathematics and Computer Science, Technical University of Sofia, 8 Kliment Ohridski, Blvd., 1000, Sofia, Bulgaria

    M. D. Todorov

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  1. V. S. Gerdjikov
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Correspondence to V. S. Gerdjikov .

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Editors and Affiliations

  1. Dept. of Mathematics and Statistics, San Diego State University, San Diego, California, USA

    Ricardo Carretero-González

  2. Dept. de Física Aplicada I, Escuela Politécnica Superior, University of Sevilla, Sevilla, Spain

    Jesús Cuevas-Maraver

  3. Dept. of Physics, University of Athens, Athens, Greece

    Dimitri Frantzeskakis

  4. Dept. of Mathematics, University of the Aegean, Samos, Greece

    Nikos Karachalios

  5. Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA

    Panayotis Kevrekidis

  6. Dept. de Física Aplicada I, E.T.S.I. Informática, University of Sevilla, Sevilla, Spain

    Faustino Palmero-Acebedo

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Gerdjikov, V.S., Todorov, M.D. (2014). N-Soliton Interactions for the Manakov System: Effects of External Potentials. In: Carretero-González, R., Cuevas-Maraver, J., Frantzeskakis, D., Karachalios, N., Kevrekidis, P., Palmero-Acebedo, F. (eds) Localized Excitations in Nonlinear Complex Systems. Nonlinear Systems and Complexity, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-02057-0_7

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