MULTI-HUMP SOLUTIONS OF SOME SINGULARLY-PERTURBED EQUATIONS OF KDV TYPE SCIE SCOPUS

Cited 5 time in WEB OF SCIENCE Cited 5 time in Scopus
Title
MULTI-HUMP SOLUTIONS OF SOME SINGULARLY-PERTURBED EQUATIONS OF KDV TYPE
Author(s)
Choi, J. W.; Lee, D. S.; Oh, S. H.; Sun, S. M.; Whang, S. I.
KIOST Author(s)
Oh, Sang Ho(오상호)
Publication Year
2014-12
Abstract
This paper studies the existence of multi-hump solutions with oscillations at infinity for a class of singularly perturbed 4th-order nonlinear ordinary differential equations with epsilon > 0 as a small parameter. When epsilon = 0, the equation becomes an equation of KdV type and has solitary-wave solutions. For epsilon > 0 small, it is proved that such equations have single-hump (also called solitary wave or homoclinic) solutions with small oscillations at infinity, which approach to the solitary-wave solutions for epsilon = 0 as c goes to zero. Furthermore, it is shown that for small epsilon > 0 the equations have two-hump solutions with oscillations at infinity. These two-hump solutions can be obtained by patching two appropriate single-hump solutions together. The amplitude of the oscillations at infinity is algebraically small with respect to epsilon as epsilon -> 0. The idea of the proof may be generalized to prove the existence of symmetric solutions of 2(n)-humps with n = 2, 3, ... , for the equations. However, this method cannot be applied to show the existence of general nonsymmetric multi-hump solutions.
ISSN
1078-0947
URI
https://sciwatch.kiost.ac.kr/handle/2020.kiost/2650
DOI
10.3934/dcds.2014.34.5181
Bibliographic Citation
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.34, no.12, pp.5181 - 5209, 2014
Publisher
AMER INST MATHEMATICAL SCIENCES
Subject
AUTONOMOUS HAMILTONIAN-SYSTEMS; GENERALIZED SOLITARY WAVE; EXPONENTIALLY SMALL ESTIMATE; CAPILLARY WATER-WAVES; KORTEWEG-DE-VRIES; SURFACE-TENSION; HOMOCLINIC SOLUTIONS; PERIODIC-ORBITS; PLETHORA; EXISTENCE
Keywords
Multi-hump waves; singularly perturbed equations
Type
Article
Language
English
Document Type
Article
Publisher
AMER INST MATHEMATICAL SCIENCES
Related Researcher
Research Interests

Coastal engineering,Physical experiment,Coastal wave,항만공학,수리실험,연안파랑

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