RT Journal Article
T1 Numerical adiabatic perturbation theory for the absolute equation
A1 Garralon-López, Rubén
A1 Rus-Mansilla, Francisco de Asís
A1 Villatoro-Machuca, Francisco Román
K1 Perturbación (Matemáticas)
K1 Matemáticas aplicadas
AB In physical applications, the absolute equation should be preferred to the widely used Rosenau–Hyman equation due to the robustness of its compactons and anticompactons interactions observed in numerical simulations with small hyperviscosity. In order to understand the effect of the hyperviscosity in solutions with multiple compactons of the equation, the adiabatic perturbation theory has been applied. For a single compacton, this theory can be solved analytically showing that the second invariant decreases for smaller than a critical value, as expected for a dissipative perturbation, but increases otherwise. This analytical prediction is in good agreement with the numerical results. In order to predict the evolution of the second invariant in time as a function of the hyperviscosity parameter for general solutions of the equation, a numerical implementation of the adiabatic perturbation theory has been developed. This adiabatic numerical prediction agrees with the evolution of the second invariant in the propagation of a single compacton, the generation of compacton trains from a truncated cosine initial condition, and compacton–compacton chase collisions. However, discrepancies emerge in other scenarios, such as the generation of a compacton train from a dilated compacton and in compacton–anticompacton chase collisions. Our findings support the use of the numerical adiabatic perturbation theory for analyzing the evolution of invariants due to hyperviscosity in multi-compacton simulations
PB Elsevier
YR 2024
FD 2024-03-28
LK https://hdl.handle.net/10630/31023
UL https://hdl.handle.net/10630/31023
LA eng
NO Rubén Garralon-López, Francisco Rus, Francisco R. Villatoro, Numerical adiabatic perturbation theory for the absolute |K|(p,p) equation, Mathematics and Computers in Simulation, 2024, , ISSN 0378-4754, https://doi.org/10.1016/j.matcom.2024.03.031. (https://www.sciencedirect.com/science/article/pii/S0378475424001113)
NO Funding for open accesscharge: Universidad deMálaga / CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026