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Non-linear fractional field equations: weak non-linearity at power-law non-locality

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Abstract

Fractional non-relativistic field equations with the derivatives of non-integer order are considered. A connection of these equations with microscopic (lattice) models is discussed. The considered equations contain non-linear terms and fractional Laplacian in the Riesz form. Using the background field method and the mean field method, we obtain corrections to linear solution and equilibrium solution caused by the weak non-linearity.

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Acknowledgments

The author expresses his gratitude to the guest editors Professor Yong Zhou, Professor Clara Ionescu, Professor J. A. Tenreiro Machado for kind invitation to contribute to a special issue titled “Fractional Dynamics and Its Applications”, in the journal Nonlinear Dynamics.

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  1. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow , 119991, Russia

    Vasily E. Tarasov

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  1. Vasily E. Tarasov
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Correspondence to Vasily E. Tarasov.

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Tarasov, V.E. Non-linear fractional field equations: weak non-linearity at power-law non-locality. Nonlinear Dyn 80, 1665–1672 (2015). https://doi.org/10.1007/s11071-014-1342-0

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