Deformations of KdV and soliton collisions

Blas H.; Ochoa R.; Suarez D. · Journal of Physics: Conference Series (2020) · DOI: 10.1088/1742-6596/1558/1/012012

Resumen

Some deformations of the integrable Korteweg-de Vries model (KdV) are associated to several towers of infinite number of asymptotically conserved charges. It has been shown that the standard KdV also exhibits infinite number of anomalous charges. In [9] there have been verified numerically the degrees of modifications of the charges around the soliton interaction regions, by computing numerically some representative anomalies, related to lowest order quasi-conservation laws, depending on the deformation parameters ϵ1,ϵ2, such that the standard KdV is recovered for ϵ1 = ϵ2=0). Here we present the numerical simulations for some values of the pair {ϵ1,ϵ2} around ϵ1 ≈ 0, ϵ2 ≈ 0, and show that the collision of two and three solitons are elastic. The KdV-type equations are quite ubiquitous and find many applications in several areas of non-linear science. © Published under licence by IOP Publishing Ltd.

Instituciones: Universidad Nacional de Ingeniería