Robustness of the absolute Rosenau-Hyman |K |(p, p) equation with non-integer p

被引:4
作者
Garralon-Lopez, Ruben [1 ]
Rus, Francisco [1 ]
Villatoro, Francisco R. [1 ]
机构
[1] Univ Malaga, Escuela Ingn Ind, Dept Lenguajes & Ciencias Comp, Malaga 29071, Spain
关键词
Compactons; Nonlinear dispersion; Numerical simulation; COMPACTONS;
D O I
10.1016/j.chaos.2023.113216
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The most widely studied equation with compactons is the Rosenau-Hyman K(p, p) equation. For non-integer p the solution becomes complex-valued in compacton collisions. In order to cope with this problem, the nonlinearity up can be substituted by |u|p-1 u, so the solution is always real-valued; the result is the so-called absolute K(p, p) equation, |K|(p, p). Here, the first numerical simulations of the collisions between compactons and anticompactons for the |K|(p, p) equation are presented. The collision is robust in both compacton- compacton and compacton-anticompacton collisions even when very small artificial viscosity is used. Our results stress that, in physical applications, the |K|(p, p) should be preferred to the K(p, p) equation.
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页数:14
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