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This article is cited in 5 scientific papers (total in 5 papers)
Compactons and Riemann waves of an extended modified Korteweg–de Vries equation with nonlinear dispersion
S. P. Popov Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia
Abstract:
The $\mathrm{K}(f^m, g^n)$ equation is studied, which generalizes the modified Korteweg–de Vries equation $\mathrm{K}(u^3, u^1)$ and the Rosenau–Hyman equation $\mathrm{K}(u^m, u^n)$ to other dependences of nonlinearity and dispersion on the solution. The considered functions $f(u)$ and $g(u)$ can be linear or can have the form of a smoothed step. It is found numerically that, depending on the form of nonlinearity and dispersion, the given equation has compacton and kovaton solutions, Riemann-wave solutions, and oscillating wave packets of two types. It is shown that the interaction between solutions of all found types occurs with the preservation of their parameters.
Key words:
KdV equation, mKdV equation, $\mathrm{K}(m, n)$ equation, Rosenau–Hyman equation, $\mathrm{K}(\cos)$ equation, the Rosenau–Pikovsky equation, compacton, kovaton, soliton, kink, Riemann wave, oscillatory waves, wave packets, multisoliton interaction.
Received: 19.10.2016 Revised: 13.03.2017
Citation:
S. P. Popov, “Compactons and Riemann waves of an extended modified Korteweg–de Vries equation with nonlinear dispersion”, Zh. Vychisl. Mat. Mat. Fiz., 58:3 (2018), 459–472; Comput. Math. Math. Phys., 58:3 (2018), 437–448
Linking options:
https://www.mathnet.ru/eng/zvmmf10696 https://www.mathnet.ru/eng/zvmmf/v58/i3/p459
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