TY - JOUR

T1 - High-order numerical method for scattering data of the Korteweg - De Vries equation

AU - Gudko, A.

AU - Gelash, A.

AU - Mullyadzhanov, R.

N1 - Funding Information: This work is funded by the Russian Foundation for Basic Research grants No. 18-02-00042 and 19-31-60028, the development of the numerical code is conducted under state contract with IT SB RAS. Publisher Copyright: © Published under licence by IOP Publishing Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/12/3

Y1 - 2020/12/3

N2 - Nonlinear wavefields governed by integrable models such as the Korteweg-De Vries (KdV) equation can be decomposed into the so-called scattering data playing the role of independent elementary harmonics evolving trivially in time. A typical scattering data portrait of a spatially localised wavefield represents nonlinear coherent wave structures (solitons) and incoherent radiation. In this work we present a fourth-order accurate algorithm to compute the scattering data within the KdV model. The method based on the Magnus expansion technique provides accurate information about soliton amplitudes, velocities and intensity of the radiation. Our tests performed using a box-shaped wavefield confirm that all components of the scattering data are computed correctly, while the test based on a single-soliton solution verifies the declared order of a numerical scheme.

AB - Nonlinear wavefields governed by integrable models such as the Korteweg-De Vries (KdV) equation can be decomposed into the so-called scattering data playing the role of independent elementary harmonics evolving trivially in time. A typical scattering data portrait of a spatially localised wavefield represents nonlinear coherent wave structures (solitons) and incoherent radiation. In this work we present a fourth-order accurate algorithm to compute the scattering data within the KdV model. The method based on the Magnus expansion technique provides accurate information about soliton amplitudes, velocities and intensity of the radiation. Our tests performed using a box-shaped wavefield confirm that all components of the scattering data are computed correctly, while the test based on a single-soliton solution verifies the declared order of a numerical scheme.

UR - http://www.scopus.com/inward/record.url?scp=85097336979&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1677/1/012011

DO - 10.1088/1742-6596/1677/1/012011

M3 - Conference article

AN - SCOPUS:85097336979

VL - 1677

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012011

T2 - 36th Siberian Thermophysical Seminar, STS 2020

Y2 - 5 October 2020 through 7 October 2020

ER -