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

Rubén Garralon-López, Francisco Rus and Francisco R. Villatoro

Chaos, Solitons & Fractals, 2023, vol. 169, issue C

Abstract: 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−1u, 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.

Keywords: Compactons; Nonlinear dispersion; Numerical simulation (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001170

DOI: 10.1016/j.chaos.2023.113216

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