MULTI-HUMP SOLUTIONS OF SOME SINGULARLY-PERTURBED EQUATIONS OF KDV TYPE
DC Field | Value | Language |
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dc.contributor.author | Choi, J. W. | - |
dc.contributor.author | Lee, D. S. | - |
dc.contributor.author | Oh, S. H. | - |
dc.contributor.author | Sun, S. M. | - |
dc.contributor.author | Whang, S. I. | - |
dc.date.accessioned | 2021-09-05T02:31:34Z | - |
dc.date.available | 2021-09-05T02:31:34Z | - |
dc.date.created | 2021-06-15 | - |
dc.date.issued | 2014-12 | - |
dc.identifier.issn | 1078-0947 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/96637 | - |
dc.description.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. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | AMER INST MATHEMATICAL SCIENCES | - |
dc.subject | AUTONOMOUS HAMILTONIAN-SYSTEMS | - |
dc.subject | GENERALIZED SOLITARY WAVE | - |
dc.subject | EXPONENTIALLY SMALL ESTIMATE | - |
dc.subject | CAPILLARY WATER-WAVES | - |
dc.subject | KORTEWEG-DE-VRIES | - |
dc.subject | SURFACE-TENSION | - |
dc.subject | HOMOCLINIC SOLUTIONS | - |
dc.subject | PERIODIC-ORBITS | - |
dc.subject | PLETHORA | - |
dc.subject | EXISTENCE | - |
dc.title | MULTI-HUMP SOLUTIONS OF SOME SINGULARLY-PERTURBED EQUATIONS OF KDV TYPE | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Choi, J. W. | - |
dc.identifier.doi | 10.3934/dcds.2014.34.5181 | - |
dc.identifier.scopusid | 2-s2.0-84902651103 | - |
dc.identifier.wosid | 000338187000009 | - |
dc.identifier.bibliographicCitation | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.34, no.12, pp.5181 - 5209 | - |
dc.relation.isPartOf | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | - |
dc.citation.title | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | - |
dc.citation.volume | 34 | - |
dc.citation.number | 12 | - |
dc.citation.startPage | 5181 | - |
dc.citation.endPage | 5209 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | AUTONOMOUS HAMILTONIAN-SYSTEMS | - |
dc.subject.keywordPlus | GENERALIZED SOLITARY WAVE | - |
dc.subject.keywordPlus | EXPONENTIALLY SMALL ESTIMATE | - |
dc.subject.keywordPlus | CAPILLARY WATER-WAVES | - |
dc.subject.keywordPlus | KORTEWEG-DE-VRIES | - |
dc.subject.keywordPlus | SURFACE-TENSION | - |
dc.subject.keywordPlus | HOMOCLINIC SOLUTIONS | - |
dc.subject.keywordPlus | PERIODIC-ORBITS | - |
dc.subject.keywordPlus | PLETHORA | - |
dc.subject.keywordPlus | EXISTENCE | - |
dc.subject.keywordAuthor | Multi-hump waves | - |
dc.subject.keywordAuthor | singularly perturbed equations | - |
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