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Born–Infeld solitons, maximal surfaces, and Ramanujan’s identities

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Abstract

We show that a Born–Infeld soliton can be realised either as a spacelike minimal graph or timelike minimal graph over a timelike plane or a combination of both away from singular points. We also obtain some exact solutions of the Born–Infeld equation from already known solutions to the maximal surface equation. Further we present a method to construct a one parameter family of complex solitons from a given one parameter family of maximal surfaces. Finally, using Ramanujan’s identities and the Weierstrass–Enneper representation of maximal surfaces, we derive further non-trivial identities.

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Authors and Affiliations

  1. International Centre for Theoretical Sciences, Bengaluru, 560 089, India

    Rukmini Dey

  2. Harish-Chandra Research Institute, HBNI, Allahabad, 211 019, India

    Rahul Kumar Singh

Authors
  1. Rukmini Dey
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  2. Rahul Kumar Singh
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Correspondence to Rahul Kumar Singh.

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Dey, R., Singh, R.K. Born–Infeld solitons, maximal surfaces, and Ramanujan’s identities. Arch. Math. 108, 527–538 (2017). https://doi.org/10.1007/s00013-016-1011-2

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  • DOI: https://doi.org/10.1007/s00013-016-1011-2

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