A non-local elliptic-hyperbolic system related to the short pulse equation. (English) Zbl 1433.35377
Summary: In this paper, we prove the well-posedness of a non-local elliptic-hyperbolic system related to the short pulse equation. It is a model which describes the evolution of the electrical field of linearly polarized continuum spectrum pulses in optical waveguides, including fused-silica telecommunication-type or photonic-crystal fibers, as well as hollow capillaries filled with transparent gases.
MSC:
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35G25 | Initial value problems for nonlinear higher-order PDEs |
| 35K55 | Nonlinear parabolic equations |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35B35 | Stability in context of PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35B45 | A priori estimates in context of PDEs |
| 78A50 | Antennas, waveguides in optics and electromagnetic theory |
Keywords:
existence; uniqueness; stability; short pulse equation; non-local formulation; Cauchy problemReferences:
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