Асимптотики за великим часом для модифiкованого рiвняння Камаси–Хольма з ненульовими крайовими умовами

Автор(и)

  • Iryna Karpenko B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine image/svg+xml

DOI:

https://doi.org/10.15407/mag18.02.224

Ключові слова:

задача Рiмана–Гiльберта, нелiнiйний метод найшвидшого спуску, солiтони

Анотація

Ми розглядаємо модифiковане рiвняння Камаси–Хольма (мКХ) mt +(( u2 - ux2 )m)x =0, m := u − uxx на осi −∞ < x < +∞, де u(x,t) задовiльняє ненульовi крайовi умови на нескiнченностi: u(x,t) → 1 при x → ±∞. Метою роботи є дослiдження асимптотики за великим часом розв’язкiв початкової задачi, застосовувуючи формалiзм задачi Рiмана–Гiльберта, що був нещодавно розроблений у [3]. Основна увага придiляється одержанню асимптотики у двох секторах пiвплощини (x,t) (t > 0), де основнi асимптотичнi члени мають вигляд модульованих та спадаючих (як t−1/2  ) тригонометричних осциляцiй, а також асимптотицi у секторi, де у поведiнцi розв’язку початкової задачi домiнують солiтони.

Mathematical Subject Classification 2010: 35Q53, 37K15, 35Q15, 35B40,
35Q51, 37K40

Посилання

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Опубліковано

2022-08-20

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(1)
Karpenko, I. . Асимптотики за великим часом для модифiкованого рiвняння Камаси–Хольма з ненульовими крайовими умовами. J. Math. Phys. Anal. Geom. 2022, 18, 224-252.

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