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On classical solutions for the fifth‐order short pulse equation
Author(s) -
Coclite Giuseppe,
Ruvo Lorenzo
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7309
Subject(s) - mathematics , cauchy problem , pulse (music) , nonlinear system , order (exchange) , mathematical analysis , initial value problem , elliptical polarization , electromagnetic pulse , physics , optics , quantum mechanics , laser , linear polarization , finance , detector , economics
The fifth‐order short pulse equation models the nonlinear propagation of optical pulses of a few oscillations duration in dielectric media. In particular, it models the propagation of circularly and elliptically polarized few‐cycle solitons in a Kerr medium. In this paper, we prove the well‐posedness of the classical solutions for the Cauchy problem associated with this equation.