AIMS Mathematics, 2019, 4(3): 437-462. doi: 10.3934/math.2019.3.437.

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Discontinuous solutions for the short-pulse master mode-locking equation

1 Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, via E. Orabona 4, 70125 Bari, Italy
2 Dipartimento di Matematica, Università di Bari, via E. Orabona 4, 70125 Bari, Italy

The short-pulse master mode-locking equation is a model for ultrafast pulse propagation in a mode-locked laser cavity in the few-femtosecond pulse regime, that is a nonlinear evolution equation. In this paper, we prove the wellposedness of the Cauchy problem associated with this equation within a class of discontinuous solutions.
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Keywords existence; uniqueness; stability; entropy solutions; conservation laws; short-pulse master mode-locking equation; Cauchy problem

Citation: Giuseppe Maria Coclite, Lorenzo di Ruvo. Discontinuous solutions for the short-pulse master mode-locking equation. AIMS Mathematics, 2019, 4(3): 437-462. doi: 10.3934/math.2019.3.437

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