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Some properties of small perturbations against a stationary solution of the nonlinear Schrödinger equation

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  • Smolyakov, Mikhail N.

Abstract

In this paper, classical small perturbations against a stationary solution of the nonlinear Schrödinger equation with the general form of nonlinearity are examined. It is shown that in order to obtain correct (in particular, conserved over time) nonzero expressions for the basic integrals of motion of a perturbation even in the quadratic order in the expansion parameter, it is necessary to consider nonlinear equations of motion for the perturbations. It is also shown that, despite the nonlinearity of the perturbations, the additivity property is valid for the integrals of motion of different nonlinear modes forming the perturbation (at least up to the second order in the expansion parameter).

Suggested Citation

  • Smolyakov, Mikhail N., 2020. "Some properties of small perturbations against a stationary solution of the nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305272
    DOI: 10.1016/j.chaos.2019.109570
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    Cited by:

    1. Smolyakov, Mikhail N., 2023. "Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature. II. The general case," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Smolyakov, Mikhail N., 2021. "Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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