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

Giuseppe Maria Coclite; Lorenzo di Ruvo; Giuseppe Maria Coclite; Lorenzo di Ruvo

doi:10.3934/math.2019.3.437

AIMS Mathematics

2019, Volume 4, Issue 3: 437-462. doi: 10.3934/math.2019.3.437

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Research article

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

Giuseppe Maria Coclite ^{1
,
,},
Lorenzo di Ruvo ²

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

Received: 09 January 2019 Accepted: 18 April 2019 Published: 08 May 2019
MSC : 35G15, 35L65, 35L05, 35A05

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

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Abstract

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.

References

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