Complex variational calculus with mean of (min, +)-analysis

Michel Gondran, Abdelouahab Kenoufi, Alexandre Gondran

Abstract


One develops a new mathematical tool, the complex (min, +)-analysis which permits to define a new variational calculus analogous to the classical one (Euler-Lagrange and Hamilton Jacobi equations), but which is well-suited for functions defined from C^n to C. We apply this complex variational calculus to Born-Infeld theory of electromagnetism and show why it does not exhibit nonlinear effects.


Keywords


Variational Calculus, Lagrangian, Hamiltonian, Action, Euler-Lagrange and Hamilton-Jacobi equations, complex (min, +)-analysis , Maxwell’s equations, Born-Infeld theory.

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References


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DOI: https://doi.org/10.5540/tema.2017.018.03.385

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TEMA - Trends in Applied and Computational Mathematics

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