2024/04/23 by Fodor, Gyula, Forgács, Péter, Mushtaq, Muneeb
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Pattern Formation and Solitons (nlin.PS)
paper · doi:10.48550/arxiv.2404.15020
The computation of the amplitude, α, of asymptotic standing wave tails of weakly delocalized, stationary solutions in a fifth-order Korteweg-de Vries equation is revisited. Assuming the coefficient of the fifth order derivative term, ε2≪1, a new derivation of the ``beyond all orders in ε'' amplitude, α, is presented. It is shown by asymptotic matching techniques, extended to higher orders in ε, that the value of α can be obtained from the asymmetry at the center of the unique solution exponentially decaying in one direction. This observation, complemented by some fundamental results of Hammersley and Mazzarino [Proc. R. Soc. Lond. A 424, 19 (1989)], not only sheds new light on the computation of α, but also greatly facilitates its numerical determination to a remarkable precision for so small values of ε, which are beyond the capabilities of standard numerical methods.