RIKKATI VA BERNULLI TENGLAMALARINI YECHISH USULLARI VA UNING TADBIQLARI
Keywords:
Rikkati tenglamasi, Bernulli tenglamasi,lemma, Backlund transformatsiyasi,differensial tenglama, NLPDE, Maple.Abstract
Rikkati-Bernoulli usuli birinchi navbatda chiziqli bo'lmagan qisman differensial tenglamalar uchun aniq harakatlanuvchi to'lqin echimlarini, soliter to'lqin echimlarini va tepalik to'lqin echimlarini qurish uchun taklif etiladi. Rikkati-Bernulli tenglamasining Beklund transformatsiyasi berilgan. Harakatlanuvchi to'lqin transformatsiyasi va Rikkati-Bernulli tenglamasidan foydalanib, chiziqli bo'lmagan qisman differensial tenglamalarni algebraik tenglamalar to'plamiga aylantirish mumkin. Nochiziqli qisman differensial tenglamalarning aniq yechimlarini algebraik tenglamalar to‘plamini yechish orqali olish mumkin. Rikkati-Bernulli tenglamasining Bäcklund transformatsiyasini qo'llash orqali yuqoridagi tenglamalar yechimlarining cheksiz ketma-ketligi olinadi. Taklif etilayotgan usul matematik fizikada ba'zi bir chiziqli bo'lmagan qisman differensial tenglamalarni yechish uchun kuchli va oddiy matematik vositani taqdim etadi.
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