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This article is cited in 2 scientific papers (total in 2 papers)
Compacton solutions of the Korteweg–de Vries equation with constrained nonlinear dispersion
S. P. Popov Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, 119333 Russia
Abstract:
The numerical solution of initial value problems is used to obtain compacton and kovaton solutions of $\mathrm{K}(f^m,g^n)$ equations generalizing the Korteweg–de Vries $\mathrm{K}(u^2,u^1)$ and Rosenau–Hyman $\mathrm{K}(u^m,u^n)$ equations to more general dependences of the nonlinear and dispersion terms on the solution $u$. The functions $f(u)$ and $g(u)$ determining their form can be linear or can have the form of a smoothed step. It is shown that peakocompacton and peakosoliton solutions exist depending on the form of the nonlinearity and dispersion. They represent transient forms combining the properties of solitons, compactons, and peakons. It is shown that these solutions can exist against an inhomogeneous and nonstationary background.
Key words:
KdV equation, mKdV equation, $\mathrm{K}(m,n)$ equation, Rosenau–Hyman equation, $\mathrm{K}(\cos)$ equation, Rosenau–Pikovsky equation, compacton, kovaton, soliton, peakon, peakocompacton.
Received: 01.12.2017 Revised: 22.04.2018
Citation:
S. P. Popov, “Compacton solutions of the Korteweg–de Vries equation with constrained nonlinear dispersion”, Zh. Vychisl. Mat. Mat. Fiz., 59:1 (2019), 158–168; Comput. Math. Math. Phys., 59:1 (2019), 150–159
Linking options:
https://www.mathnet.ru/eng/zvmmf10825 https://www.mathnet.ru/eng/zvmmf/v59/i1/p158
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Abstract page: | 127 | References: | 19 |
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