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

Author

Listed:
  • Garralon-López, Rubén
  • Rus, Francisco
  • Villatoro, Francisco R.

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.

Suggested Citation

  • Garralon-López, Rubén & Rus, Francisco & Villatoro, Francisco R., 2023. "Robustness of the absolute Rosenau–Hyman |K|(p,p) equation with non-integer p," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001170
    DOI: 10.1016/j.chaos.2023.113216
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    References listed on IDEAS

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    1. Iqbal, A. & Naeem, I., 2022. "Generalized compacton equation, conservation laws and exact solutions," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    2. Rus, Francisco & Villatoro, Francisco R., 2007. "Padé numerical method for the Rosenau–Hyman compacton equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 188-192.
    3. Ismail, M.S. & Taha, T.R., 1998. "A numerical study of compactons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(6), pages 519-530.
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