Yarim o‘qda Korteveg–de Friz (KdF) tenglamasi, boshlang‘ich–chegaraviy masala, yechim usullari va amaliy talqinlar

Eshchanova Gulchehra Sheribbayevna

Abu Rayhon Beruniy nomidagi Urganch davlat universiteti huzuridagi fizika-matematika va informatika fanlariga ixtisoslashtirilgan maktab direktori

Keywords: KdF tenglamasi, yarim o‘q, boshlang‘ich–chegaraviy masala, Dirixle sharti, Neyman sharti, Fokas usuli, soliton, dispersiya.

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Abstract

Ushbu tezisda Korteveg–de Friz tenglamasining yarim o‘q (x ≥ 0) sohasida qo‘yiladigan boshlang‘ich–chegaraviy masalasi (initial-boundary value problem, IBVP) yoritiladi. KdF tenglamasi nochiziqli dispersiv jarayonlarni, xususan sayoz suv to‘lqinlari, plazmadagi ion-akustik to‘lqinlar va elastik muhitdagi impulslarning tarqalishini modellashtirishda klassik model hisoblanadi. Cheksiz butun o‘qdagi masalalarga nisbatan yarim o‘qda yechim topish murakkabroq: bunga sabab chegaradagi shartlar nolinеarlik bilan birikib, spektral bog‘lanishlarni keltirib chiqarishidir. Tezisda chegaraviy shartlarning turlari, moslik (compatibility) talablari, hamda yechim qurishning analitik (teskari sochilish, Fokasning yagona transformi) va sonli (diskret sxemalar) yondashuvlari haqida tizimli tasavvur beriladi.

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