ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT

Результат исследований: Вклад в журналСтатьяНаучно-исследовательскаярецензирование

Аннотация

We consider a three-dimensional nonlinear wave equation with the source term smoothly changing over time and space due to a small parameter. The behavior of solutions of this PDE near the typical “butterfly” catastrophe point is studied. In the framework of matched asymptotic expansions method we derive a nonlinear ODE of the second order depending on three parameters to search for the special solution describing the rapid restructuring of the solution of the PDE in a small neighborhood of the catastrophe point, matching with expansion in a more outer layer. Numerical integration curves of the equation for the leading term of the inner asymptotic expansion are obtained.
Язык оригиналаАнглийский
Страницы (с-по)127-140
Число страниц14
ЖурналURAL MATHEMATICAL JOURNAL
Том2
Номер выпуска2(3)
DOI
СостояниеОпубликовано - 2016

Отпечаток

Catastrophe
Numerical integration
Nonlinear ODE
Curve
Matched Asymptotic Expansions
Nonlinear Wave Equation
Behavior of Solutions
Source Terms
Small Parameter
Asymptotic Expansion
Three-dimensional
Term
Framework

ГРНТИ

  • 27.00.00 МАТЕМАТИКА

Уровень публикации

  • Перечень ВАК

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abstract = "We consider a three-dimensional nonlinear wave equation with the source term smoothly changing over time and space due to a small parameter. The behavior of solutions of this PDE near the typical “butterfly” catastrophe point is studied. In the framework of matched asymptotic expansions method we derive a nonlinear ODE of the second order depending on three parameters to search for the special solution describing the rapid restructuring of the solution of the PDE in a small neighborhood of the catastrophe point, matching with expansion in a more outer layer. Numerical integration curves of the equation for the leading term of the inner asymptotic expansion are obtained.",
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ON SOME NUMERICAL INTEGRATION CURVES FOR PDE IN NEIGHBORHOOD OF "BUTTERFLY" CATASTROPHE POINT. / Khachay, Oleg Y.; Nosov, Pavel A.

В: URAL MATHEMATICAL JOURNAL, Том 2, № 2(3), 2016, стр. 127-140.

Результат исследований: Вклад в журналСтатьяНаучно-исследовательскаярецензирование

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AB - We consider a three-dimensional nonlinear wave equation with the source term smoothly changing over time and space due to a small parameter. The behavior of solutions of this PDE near the typical “butterfly” catastrophe point is studied. In the framework of matched asymptotic expansions method we derive a nonlinear ODE of the second order depending on three parameters to search for the special solution describing the rapid restructuring of the solution of the PDE in a small neighborhood of the catastrophe point, matching with expansion in a more outer layer. Numerical integration curves of the equation for the leading term of the inner asymptotic expansion are obtained.

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