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Numerical simulation of soliton gas within the Korteweg-de Vries type equations

Диденкулова, Екатерина Геннадьевна ; Кокорина, Анна Витальевна ; Слюняев, Алексей Викторович

Вычислительные технологии, 2019-04 (2(24)), p.52-66 [Periódico revisado por pares]

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  • Título:
    Numerical simulation of soliton gas within the Korteweg-de Vries type equations
  • Autor: Диденкулова, Екатерина Геннадьевна ; Кокорина, Анна Витальевна ; Слюняев, Алексей Викторович
  • É parte de: Вычислительные технологии, 2019-04 (2(24)), p.52-66
  • Descrição: Приведены детали численной схемы и способа задания начальных условий для моделирования нерегулярной динамики ансамблей солитонов в рамках уравнений типа Кортевега-де Вриза на примере модифицированного уравнения Кортевега-де Вриза с фокусирующим типом нелинейности. Дано качественное описание эволюции статистических характеристик для ансамблей солитонов одной и разных полярностей. Обсуждаются результаты тестовых экспериментов по столкновению большого числа солитонов. The details of the numerical scheme and the method of specifying the initial conditions for the simulation of the irregular dynamics of soliton ensembles within the framework of equations of the Korteweg - de Vries type are given using the example of the modified Korteweg - de Vries equation with a focusing type of nonlinearity. The numerical algorithm is based on a pseudo-spectral method with implicit integration over time and uses the Crank-Nicholson scheme for improving the stability property. The aims of the research are to determine the relationship between the spectral composition of the waves (the Fourier spectrum or the spectrum of the associated scattering problem) and their probabilistic properties, to describe transient processes and the equilibrium states. The paper gives a qualitative description of the evolution of statistical characteristics for ensembles of solitons of the same and different polarities, obtained as a result of numerical simulations; the probability distributions for wave amplitudes are also provided. The results of test experiments on the collision of a large number of solitons are discussed: the choice of optimal conditions and the manifestation of numerical artifacts caused by insufficient accuracy of the discretization. The numerical scheme used turned out to be extremely suitable for the class of the problems studied, since it ensures good accuracy in describing collisions of solitons with a short computation time.
  • Idioma: Russo
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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