Compactons and Riemann Waves of an Extended Modified Korteweg-de Vries Equation with Nonlinear Dispersion

被引：4

作者：

Popov, S. P. ^{[1
]}

机构：

[1] Russian Acad Sci, Dorodnicyn Comp Ctr, Fed Res Ctr Comp Sci & Control, Moscow 119333, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2018年 / 58卷 / 03期

关键词：

KdV equation; mKdV equation; K(m; n); equation; Rosenau-Hyman equation; K(cos) equation; the Rosenau-Pikovsky equation; compacton; kovaton; soliton; kink; Riemann wave; oscillatory waves; wave packets; multisoliton interaction; SOLITON-SOLUTIONS; GALERKIN METHODS; DOMAIN-WALLS; DYNAMICS; KOVATONS;

D O I：

10.1134/S0965542518030107

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The K(f (m) , g (n) ) equation is studied, which generalizes the modified Korteweg-de Vries equation K(u (3), u (1)) and the Rosenau-Hyman equation 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.

引用

页码：437 / 448

页数：12

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