Existence of Multi-Pulses of the Regularized Short-Pulse and Ostrovsky Equations

The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed vector fields. Similar to the non-singular case, the sign of a geometric condition that involves the first integral decides whether multi-pu...

Full description

Saved in:
Bibliographic Details
Published in:Journal of dynamics and differential equations 2009-12, Vol.21 (4), p.607-622
Main Authors: Manukian, Vahagn, Costanzino, Nicola, Jones, Christopher K. R. T., Sandstede, Björn
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c288t-752d4f84cde8ac46aa5f7cb9ff93b350a346a077a5cf2bea43082b105448380b3
cites cdi_FETCH-LOGICAL-c288t-752d4f84cde8ac46aa5f7cb9ff93b350a346a077a5cf2bea43082b105448380b3
container_end_page 622
container_issue 4
container_start_page 607
container_title Journal of dynamics and differential equations
container_volume 21
creator Manukian, Vahagn
Costanzino, Nicola
Jones, Christopher K. R. T.
Sandstede, Björn
description The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed vector fields. Similar to the non-singular case, the sign of a geometric condition that involves the first integral decides whether multi-pulses exist or not. The proof utilizes a combination of geometric singular perturbation theory and Lyapunov–Schmidt reduction through Lin’s method. The motivation for considering orbit flips in singularly perturbed systems comes from the regularized short-pulse equation and the Ostrovsky equation, which both fit into this framework and are shown here to support multi-pulses.
doi_str_mv 10.1007/s10884-009-9147-4
format article
fullrecord <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s10884_009_9147_4</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s10884_009_9147_4</sourcerecordid><originalsourceid>FETCH-LOGICAL-c288t-752d4f84cde8ac46aa5f7cb9ff93b350a346a077a5cf2bea43082b105448380b3</originalsourceid><addsrcrecordid>eNp9UMlOwzAQtRBIlMIHcPMPGMZLsH1EVVmkoiKWs-U4dptSErAdRPl6XIUzp1neopmH0DmFCwogLxMFpQQB0ERTIYk4QBNaSUY0Y-yw9CCASKbFMTpJaQOFqLieoMf5d5uy75zHfcAPwza35HHYJp_2c157_ORXw9bG9sc3-Hndxzzi2HYNXqYc-6_0tsPzz8Hmtu_SKToKtuBnf3WKXm_mL7M7slje3s-uF8QxpTKRFWtEUMI1XlknrqytgnS1DkHzmldgedmBlLZygdXeCg6K1RQqIRRXUPMpoqOvi31K0QfzEdt3G3eGgtlHYsZITPnU7CMxomjYqEmF2618NJt-iF058x_RLw40ZPI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Existence of Multi-Pulses of the Regularized Short-Pulse and Ostrovsky Equations</title><source>Springer Nature</source><creator>Manukian, Vahagn ; Costanzino, Nicola ; Jones, Christopher K. R. T. ; Sandstede, Björn</creator><creatorcontrib>Manukian, Vahagn ; Costanzino, Nicola ; Jones, Christopher K. R. T. ; Sandstede, Björn</creatorcontrib><description>The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed vector fields. Similar to the non-singular case, the sign of a geometric condition that involves the first integral decides whether multi-pulses exist or not. The proof utilizes a combination of geometric singular perturbation theory and Lyapunov–Schmidt reduction through Lin’s method. The motivation for considering orbit flips in singularly perturbed systems comes from the regularized short-pulse equation and the Ostrovsky equation, which both fit into this framework and are shown here to support multi-pulses.</description><identifier>ISSN: 1040-7294</identifier><identifier>EISSN: 1572-9222</identifier><identifier>DOI: 10.1007/s10884-009-9147-4</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Applications of Mathematics ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Partial Differential Equations</subject><ispartof>Journal of dynamics and differential equations, 2009-12, Vol.21 (4), p.607-622</ispartof><rights>Springer Science+Business Media, LLC 2009</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c288t-752d4f84cde8ac46aa5f7cb9ff93b350a346a077a5cf2bea43082b105448380b3</citedby><cites>FETCH-LOGICAL-c288t-752d4f84cde8ac46aa5f7cb9ff93b350a346a077a5cf2bea43082b105448380b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27900,27901</link.rule.ids></links><search><creatorcontrib>Manukian, Vahagn</creatorcontrib><creatorcontrib>Costanzino, Nicola</creatorcontrib><creatorcontrib>Jones, Christopher K. R. T.</creatorcontrib><creatorcontrib>Sandstede, Björn</creatorcontrib><title>Existence of Multi-Pulses of the Regularized Short-Pulse and Ostrovsky Equations</title><title>Journal of dynamics and differential equations</title><addtitle>J Dyn Diff Equat</addtitle><description>The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed vector fields. Similar to the non-singular case, the sign of a geometric condition that involves the first integral decides whether multi-pulses exist or not. The proof utilizes a combination of geometric singular perturbation theory and Lyapunov–Schmidt reduction through Lin’s method. The motivation for considering orbit flips in singularly perturbed systems comes from the regularized short-pulse equation and the Ostrovsky equation, which both fit into this framework and are shown here to support multi-pulses.</description><subject>Applications of Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><issn>1040-7294</issn><issn>1572-9222</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp9UMlOwzAQtRBIlMIHcPMPGMZLsH1EVVmkoiKWs-U4dptSErAdRPl6XIUzp1neopmH0DmFCwogLxMFpQQB0ERTIYk4QBNaSUY0Y-yw9CCASKbFMTpJaQOFqLieoMf5d5uy75zHfcAPwza35HHYJp_2c157_ORXw9bG9sc3-Hndxzzi2HYNXqYc-6_0tsPzz8Hmtu_SKToKtuBnf3WKXm_mL7M7slje3s-uF8QxpTKRFWtEUMI1XlknrqytgnS1DkHzmldgedmBlLZygdXeCg6K1RQqIRRXUPMpoqOvi31K0QfzEdt3G3eGgtlHYsZITPnU7CMxomjYqEmF2618NJt-iF058x_RLw40ZPI</recordid><startdate>20091201</startdate><enddate>20091201</enddate><creator>Manukian, Vahagn</creator><creator>Costanzino, Nicola</creator><creator>Jones, Christopher K. R. T.</creator><creator>Sandstede, Björn</creator><general>Springer US</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20091201</creationdate><title>Existence of Multi-Pulses of the Regularized Short-Pulse and Ostrovsky Equations</title><author>Manukian, Vahagn ; Costanzino, Nicola ; Jones, Christopher K. R. T. ; Sandstede, Björn</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c288t-752d4f84cde8ac46aa5f7cb9ff93b350a346a077a5cf2bea43082b105448380b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Applications of Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Manukian, Vahagn</creatorcontrib><creatorcontrib>Costanzino, Nicola</creatorcontrib><creatorcontrib>Jones, Christopher K. R. T.</creatorcontrib><creatorcontrib>Sandstede, Björn</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of dynamics and differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Manukian, Vahagn</au><au>Costanzino, Nicola</au><au>Jones, Christopher K. R. T.</au><au>Sandstede, Björn</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence of Multi-Pulses of the Regularized Short-Pulse and Ostrovsky Equations</atitle><jtitle>Journal of dynamics and differential equations</jtitle><stitle>J Dyn Diff Equat</stitle><date>2009-12-01</date><risdate>2009</risdate><volume>21</volume><issue>4</issue><spage>607</spage><epage>622</epage><pages>607-622</pages><issn>1040-7294</issn><eissn>1572-9222</eissn><abstract>The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed vector fields. Similar to the non-singular case, the sign of a geometric condition that involves the first integral decides whether multi-pulses exist or not. The proof utilizes a combination of geometric singular perturbation theory and Lyapunov–Schmidt reduction through Lin’s method. The motivation for considering orbit flips in singularly perturbed systems comes from the regularized short-pulse equation and the Ostrovsky equation, which both fit into this framework and are shown here to support multi-pulses.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s10884-009-9147-4</doi><tpages>16</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1040-7294
ispartof Journal of dynamics and differential equations, 2009-12, Vol.21 (4), p.607-622
issn 1040-7294
1572-9222
language eng
recordid cdi_crossref_primary_10_1007_s10884_009_9147_4
source Springer Nature
subjects Applications of Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
title Existence of Multi-Pulses of the Regularized Short-Pulse and Ostrovsky Equations
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-24T04%3A03%3A56IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref_sprin&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Existence%20of%20Multi-Pulses%20of%20the%20Regularized%20Short-Pulse%20and%20Ostrovsky%20Equations&rft.jtitle=Journal%20of%20dynamics%20and%20differential%20equations&rft.au=Manukian,%20Vahagn&rft.date=2009-12-01&rft.volume=21&rft.issue=4&rft.spage=607&rft.epage=622&rft.pages=607-622&rft.issn=1040-7294&rft.eissn=1572-9222&rft_id=info:doi/10.1007/s10884-009-9147-4&rft_dat=%3Ccrossref_sprin%3E10_1007_s10884_009_9147_4%3C/crossref_sprin%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c288t-752d4f84cde8ac46aa5f7cb9ff93b350a346a077a5cf2bea43082b105448380b3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true