PEDLOSKY BAROKLIN TO‘LQIN AMPLITUDASI TENGLAMALARI
DOI:
https://doi.org/10.5281/zenodo.20311502Keywords:
baroklin beqarorlik, AB tizimi, sine-Gordon tenglamasi, soliton, breather, halokatli to‘lqin, Darboux transformatsiyasi.Abstract
Ushbu maqolada ikki qatlamli geofizik suyuqlikdagi baroklin beqaror atrofidagi to‘lqin paketlarining nochiziqli dinamikasi Pedlosky tomonidan taklif qilingan amplituda tenglamalari yordamida matematik tahlil qilingan. Gibbon, James va Morozning o‘zgaruvchi almashtirish usuli yordamida Pedlosky tenglamalarining sine-Gordon tenglamasiga ekvivalentligi isbot qilinadi. AB tizimining matematik tuzilishi, saqlanish qonunlari, Darboux transformatsiyasi va soliton yechimlari etilgan.References
Pedlosky J., Finite-amplitude baroclinic waves, Journal of Atmospheric Sciences, 27 (1970), 15–30.
Gibbon J. D., James I. N., Moroz I. M., An example of soliton behaviour in a rotating baroclinic fluid, Proceedings of the Royal Society of London Series A, 367 (1979), 219–237.
Gibbon J. D., McGuinness M. J., Amplitude equations at the critical points of unstable dispersive physical systems, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 377 (1981), 185–219.
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Su J.-J., Gao Y.-T., Ding C.-C., Darboux transformations and rogue wave solutions of a generalized AB system for the geophysical flows, Applied Mathematics Letters, 88 (2019), 201–208.
Su J.-J., Zhang S., Nth-order rogue waves for the ab system via the determinants, Applied Mathematics Letters, 112 (2021), 106714.
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