Discontinuous solutions for the generalized short pulse equation

Giuseppe Maria Coclite; Lorenzo di Ruvo

doi:10.3934/eect.2019036

Article Contents

2019, Volume 8, Issue 4: 737-753. Doi: 10.3934/eect.2019036

This issue Previous Article Well-posedness and asymptotic behavior of the dissipative Ostrovsky equation Next Article On some nonlinear problem for the thermoplate equations

Discontinuous solutions for the generalized short pulse equation

Giuseppe Maria Coclite^1, , and
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

^* Corresponding author: G. M. Coclite
^* Corresponding author: G. M. Coclite

Received: June 30, 2018

Revised: December 31, 2018

Early access: June 2019

Published: June 2019

The authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM)

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Abstract

The generalized short pulse equation is a non-slowly-varying envelope approximation model that describes the physics of few-cycle-pulse optical solitons. This 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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Mathematics Subject Classification: Primary: 35G15, 35L65, 35L05; Secondary: 35A05.

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