Exact Solutions of Nonlinear Equations in Mathematical Physics via Negative Power Expansion Method

Автор(и)

  • Bo Xu School of Mathematics, China University of Mining and Technology, Xuzhou 221116,China
    School of Educational Science, Bohai University, Jinzhou 121013, China
  • Sheng Zhang School of Mathematics and Physics, Bohai University, Jinzhou 121013, China

DOI:

https://doi.org/10.15407/mag17.03.369

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 решiтки

Анотація

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

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Xu, B.; Zhang, S. Exact Solutions of Nonlinear Equations in Mathematical Physics via Negative Power Expansion Method. Журн. мат. фіз. анал. геом. 2021, 17, 369-387.

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