Exact Solutions of Nonlinear Equations in Mathematical Physics via Negative Power Expansion Method
DOI:
https://doi.org/10.15407/mag17.03.369Анотація
У статтi представлено прямий метод, що називається методом негативного розширення потужностi (НРП), який застосовано для побудови точних розв’язкiв нелiнiйних рiвнянь математичної фiзики. Запропонований метод (НРП) є також ефективним для зв’язаних рiвнянь, рiвнянь зi змiнним коефiцiєнтом та деяких iнших спецiальних видiв рiвнянь. Щоб показати ефективнiсть даного методу, було розглянуто (2 + 1)-вимiрне дисперсiйне рiвняння для довгої хвилi, рiвняння Маккарi, рiвняння Цицейки–Додда–Буллоу, рiвняння Савада–Котера зi змiнними коефiцiєнтами та два рiвняння решiтки. У результатi одержано точнi розв’язки, включаючи розв’язки рiвняння бiжної хвилi, рiвняння небiжної хвилi та напiвдискретнi розв’язки. У статтi показано, що метод НРП - це простий та ефективний спосiб розв’язку нелiнiйних рiвнянь в математичнiй фiзицi.Mathematics Subject Classification: 35Q51, 35J99, 68W30
Ключові слова:
точний розв’язок, метод НРП, (2 1)-вимiрне дисперсiйне рiвняння для довгої хвилi, рiвняння Маккарi, рiвняння Цицейки–Додда–Буллоу, рiвняння Савада–Котера зi змiнними коефiцiєнтами, рiвняння решiткиПосилання
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