Open AccessDeformations of KdV and soliton collisions
Author(s) -
Harold Blas,
R. Ochoa,
Diego Berdeja Suárez
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1558/1/012012
Subject(s) - algorithm , korteweg–de vries equation , physics , computer science , nonlinear system , quantum mechanics
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 { ∈ 1 , ∈ 2 } , such that the standard KdV is recovered for ( ∈ 1 = ∈ 2 = 0 ) . Here we present the numerical simulations for some values of the pair { ∈ 1 , ∈ 2 } around ∈ 1 ≈ 0 , ∈ 2 ≈ 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.