Open AccessEXISTENCE OF TRAVELING WAVE FRONTS FOR A GENERALIZED KDV–MKDV EQUATION
Author(s) -
Ying Xu,
Zhijiang Du
Publication year - 2014
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2014.956827
Subject(s) - korteweg–de vries equation , mathematics , traveling wave , kernel (algebra) , mathematical analysis , perturbation (astronomy) , convolution (computer science) , fredholm integral equation , integral equation , pure mathematics , nonlinear system , physics , artificial neural network , quantum mechanics , machine learning , computer science
This paper deals with the existence of traveling wave fronts for a generalized KdV–mKdV equation. We first establish the existence of traveling wave solutions for the equation without delay, and then we prove the existence of traveling wave fronts for the equation with a special local delay convolution kernel and a special nonlocal delay convolution kernel by using geometric singular perturbation theory, Fredholm theory and the linear chain trick.