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One-parameter family of solitons from minimal surfaces

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Abstract

In this paper, we discuss a one parameter family of complex Born–Infeld solitons arising from a one parameter family of minimal surfaces. The process enables us to generate a new solution of the B–I equation from a given complex solution of a special type (which are abundant). We illustrate this with many examples. We find that the action or the energy of this family of solitons remains invariant in this family and find that the well-known Lorentz symmetry of the B–I equations is responsible for it.

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Acknowledgement

The first author would like to thank Professor Randall Kamien for the observation that the minimal surface equation is just the wick rotated Born–Infeld equation.

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Authors and Affiliations

  1. School of Mathematics, Harish Chandra Research Institute, Allahabad, 211 019, India

    RUKMINI DEY & PRADIP KUMAR

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  1. RUKMINI DEY
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  2. PRADIP KUMAR
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Correspondence to RUKMINI DEY.

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DEY, R., KUMAR, P. One-parameter family of solitons from minimal surfaces. Proc Math Sci 123, 55–65 (2013). https://doi.org/10.1007/s12044-013-0115-x

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  • DOI: https://doi.org/10.1007/s12044-013-0115-x

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