Interaction of solitons and the effect of radiation for the generalized KdV equation

Martín G. García-Alvarado; Georgii A. Omel'yanov

doi:10.1016/j.cnsns.2013.06.024

Interaction of solitons and the effect of radiation for the generalized KdV equation

Martín G. García-Alvarado^*
, Georgii A. Omel'yanov

^*Autor correspondiente de este trabajo

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

12 Citas (Scopus)

Resumen

We consider the generalized KdV equation with nonlinearity u⁴ and small dispersion ε. Our main result consists in the conclusion that, in the leading term with respect to ε, the solitary waves interact in this model like KdV solitons but both small corrections of the soliton parameters and small radiation term appear as a result of the waves collision. Our main tool is the numerical simulation.

Idioma original	Inglés
Páginas (desde-hasta)	2724-2733
Número de páginas	10
Publicación	Communications in Nonlinear Science and Numerical Simulation
Volumen	19
N.º	8
DOI	https://doi.org/10.1016/j.cnsns.2013.06.024
Estado	Publicada - ago. 2014

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title = "Interaction of solitons and the effect of radiation for the generalized KdV equation",

abstract = "We consider the generalized KdV equation with nonlinearity u4 and small dispersion ε. Our main result consists in the conclusion that, in the leading term with respect to ε, the solitary waves interact in this model like KdV solitons but both small corrections of the soliton parameters and small radiation term appear as a result of the waves collision. Our main tool is the numerical simulation.",

keywords = "Finite differences scheme, Generalized Korteweg-de Vries equation, Interaction, Soliton, Weak asymptotics method",

author = "Garc{\'i}a-Alvarado, \{Mart{\'i}n G.\} and Omel'yanov, \{Georgii A.\}",

note = "Funding Information: The research was supported by SEP-CONACYT under Grant 178690 (Mexico). ",

year = "2014",

month = aug,

doi = "10.1016/j.cnsns.2013.06.024",

language = "Ingl{\'e}s",

volume = "19",

pages = "2724--2733",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

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number = "8",

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TY - JOUR

T1 - Interaction of solitons and the effect of radiation for the generalized KdV equation

AU - García-Alvarado, Martín G.

AU - Omel'yanov, Georgii A.

N1 - Funding Information: The research was supported by SEP-CONACYT under Grant 178690 (Mexico).

PY - 2014/8

Y1 - 2014/8

N2 - We consider the generalized KdV equation with nonlinearity u4 and small dispersion ε. Our main result consists in the conclusion that, in the leading term with respect to ε, the solitary waves interact in this model like KdV solitons but both small corrections of the soliton parameters and small radiation term appear as a result of the waves collision. Our main tool is the numerical simulation.

AB - We consider the generalized KdV equation with nonlinearity u4 and small dispersion ε. Our main result consists in the conclusion that, in the leading term with respect to ε, the solitary waves interact in this model like KdV solitons but both small corrections of the soliton parameters and small radiation term appear as a result of the waves collision. Our main tool is the numerical simulation.

KW - Finite differences scheme

KW - Generalized Korteweg-de Vries equation

KW - Interaction

KW - Soliton

KW - Weak asymptotics method

UR - https://www.scopus.com/pages/publications/84894300990

U2 - 10.1016/j.cnsns.2013.06.024

DO - 10.1016/j.cnsns.2013.06.024

M3 - Artículo

SN - 1007-5704

VL - 19

SP - 2724

EP - 2733

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 8

ER -

Interaction of solitons and the effect of radiation for the generalized KdV equation

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