کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9501662 | 1338769 | 2005 | 80 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On a class of solutions of KdV
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: On a class of solutions of KdV On a class of solutions of KdV](/preview/png/9501662.png)
چکیده انگلیسی
Practically every book on the Inverse Scattering Transform method for solving the Cauchy problem for KdV and other integrable systems refers to this method as nonlinear Fourier transform. If this is indeed so, the method should lead to a nonlinear analogue of the Fourier expansion formula u(t,x)=â«-â+âu^(k)eikx-Ï(k)tdk. In this paper a special class of solutions of KdV whose role is similar to that of eikx-Ï(k)t is discussed. The theory of these solutions, referred to here as harmonic breathers, is developed and it is shown that these solutions may be used to construct more general solutions of KdV similarly to how the functions eikx-Ï(t) are used to perform the same task in the theory of Fourier transform. A nonlinear superposition formula for general solutions of KdV similar to the Fourier expansion formula is conjectured.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 213, Issue 1, 1 June 2005, Pages 1-80
Journal: Journal of Differential Equations - Volume 213, Issue 1, 1 June 2005, Pages 1-80
نویسندگان
M. Kovalyov,