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The concept of quasi-integrability for modified non-linear Schrödinger models

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Abstract

We consider modifications of the nonlinear Schrödinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an infinite number of quasi-conserved charges which present intriguing properties in relation to very specific space-time parity transformations. For the case of two-soliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of non-linear science. We make a detailed numerical study of the modified NLS potential of the form V ~ (|ψ|2)2+ε, with ε being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasi-integrability concepts recently proposed in the context of modifications of the sine-Gordon model remain valid for perturbations of the NLS model.

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Authors and Affiliations

  1. Instituto de Física de São Carlos, IFSC/USP, Universidade de São Paulo, Caixa Postal 369, CEP 13560-970, São Carlos, SP, Brazil

    L. A. Ferreira & G. Luchini

  2. Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE, U.K.

    Wojtek J. Zakrzewski

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  1. L. A. Ferreira
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  2. G. Luchini
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  3. Wojtek J. Zakrzewski
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Correspondence to L. A. Ferreira.

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ArXiv ePrint: 1206.5808

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Ferreira, L.A., Luchini, G. & Zakrzewski, W.J. The concept of quasi-integrability for modified non-linear Schrödinger models. J. High Energ. Phys. 2012, 103 (2012). https://doi.org/10.1007/JHEP09(2012)103

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