H²-solutions for an Ostrosky–Hunter type equation

Abstract

The Ostrosky–Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth, for the evolution of nonlinear propagation of optical pulses of a few oscillations duration in dielectric media, and for the evolution of the propagation of ultra-short light pulses in silica optical fibers. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem, associated with this equation.

Keywords:

• Existence
• uniqueness
• stability
• Ostrosky–Hunter type equations
• Cauchy problem

2020 Mathematics Subject Classifications:

• 35G25
• 35K55

Acknowledgments

GMC is member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). GMC has been partially supported by the Project funded under the National Recovery and Resilience Plan (NRRP), Mission 4, Component 2, Investment 1.4 (Call for tender No. 3138 of 16/12/2021), of Italian Ministry of University and Research funded by the European Union (NextGenerationEU Award, No. CN000023, Concession Decree No. 1033 of 17/06/2022) adopted by the Italian Ministry of University and Research (CUP D93C22000410001), Centro Nazionale per la Mobilità Sostenibile. He has also been supported by the Italian Ministry of Education, University and Research under the Programme ‘Department of Excellence’ Legge 232/2016 (CUP D93C23000100001), and by the Research Project of National Relevance ‘Evolution problems involving interacting scales’ granted by the Italian Ministry of Education, University and Research (MIUR PRIN 2022, project code 2022M9BKBC, CUP D53D23005880006). GMC expresses his gratitude to the HIAS – Hamburg Institute for Advanced Study for their warm hospitality.

Disclosure statement

No potential conflict of interest was reported by the author(s).