Asymptotics as \(t\to\infty\) of the solutions of nonlinear equations with nonsmall initial perturbations (Q1360821)
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scientific article; zbMATH DE number 1037775
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotics as \(t\to\infty\) of the solutions of nonlinear equations with nonsmall initial perturbations |
scientific article; zbMATH DE number 1037775 |
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Asymptotics as \(t\to\infty\) of the solutions of nonlinear equations with nonsmall initial perturbations (English)
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27 January 1998
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The authors find the asymptotics for the initial value problem for the equation \(u_t+2uu_x+Ku=0\), where \(K\) is a linear pseudodifferential operator. The conditions on \(K\) allow to consider the well-known Korteweg-de-Vries, Burgers, Benjamin-Ono, Kuramotto-Sivashinski, and Ott-Sudan-Ostrovsky equations. The method is new and uses the Fourier transform.
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Cauchy problem
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pseudodifferential operator
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Burgers equation
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Korteweg-de-Vries Eeuation
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