Paper Info
Title
A New Type Of Solitary Wave Solution Of The Mkdv Equation Under Singular Perturbations
Abstract
In this work, we examine the solitary wave solutions of the mKdV equation with small singular perturbations. Our analysis is a combination of geometric singular perturbation theory and Melnikov's method. Our result shows that two families of solitary wave solutions of rnKdV equation, having arbitrary positive wave speeds and infinite boundary limits, persist for selected wave speeds after small singular perturbations. More importantly, a new type of solitary wave solution possessing both valley and peak, named as breather in physics, which corresponds to a big homoclinic loop of the associated dynamical system is observed. It reveals an exotic phenomenon and exhibits rich dynamics of the perturbed nonlinear wave equation. Numerical simulations are performed to further detect the wave speeds of the persistent solitary waves and the nontrivial one with both valley and peak.
Year
DOI
Venue
2020
10.1142/S021812742050162X
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
Solitary wave solution, homoclinic bifurcation, geometric singular perturbation method, Melnikov's function
Journal
30
Issue
ISSN
Citations 
11
0218-1274
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Lijun Zhang124537.10
Maoan Han229561.51
Mingji Zhang311.72
Chaudry Masood Khalique47416.95