{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T23:31:51Z","timestamp":1649115111311},"reference-count":79,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,10]]},"abstract":" To give rigorous mathematical proofs of chaotic behaviors in a given system, it is necessary to identify the homoclinic structures in the system. In this tutorial review, methods for constructing explicit solutions for nonlinear partial differential equations are presented, with more emphasis placed on those utilizing complete integrability associated with soliton equations. As an extended application, homoclinic orbits to spatial uniform plane waves of coupled modified nonlinear Schr\u00f6dinger equations are obtained via the dressing method. During the procedure, it is necessary to introduce the Lax pair for these coupled equations, as well as its Floquet spectral analysis and corresponding Bloch functions. <\/jats:p>","DOI":"10.1142\/s0218127406016471","type":"journal-article","created":{"date-parts":[[2006,12,8]],"date-time":"2006-12-08T06:26:15Z","timestamp":1165559175000},"page":"2799-2813","source":"Crossref","is-referenced-by-count":3,"title":["A BRIEF SURVEY ON CONSTRUCTING HOMOCLINIC STRUCTURES OF SOLITON EQUATIONS"],"prefix":"10.1142","volume":"16","author":[{"given":"RANCHAO","family":"WU","sequence":"first","affiliation":[{"name":"Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China"},{"name":"School of Mathematics and Computational Science, Anhui University, Hefei 230039, P. R. China"}]},{"given":"JIANHUA","family":"SUN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1974534249"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/0150021"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623998"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(95)00434-3"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.84.887"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02098447"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02097398"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.3367\/UFNr.0149.198607d.0449"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0294-1449(97)89300-6"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0080578"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.50.1095"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(88)90580-4"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(86)90066-0"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2004.02.014"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-81448-8"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2004.01.023"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(00)00299-8"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(95)00223-5"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402005303"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1023\/B:JODY.0000041282.14930.7a"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/20\/8\/020"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.65.876"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(03)00758-8"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(90)90142-C"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-69969-9"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1063\/1.525509"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1007\/s003329910012"},{"key":"rf28","first-page":"24","volume":"226","author":"Forest M. G.","journal-title":"Phys. Lett. A"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2005.04.017"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.19.1095"},{"key":"rf31","volume-title":"Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields","author":"Guckenheimer J.","year":"1990"},{"key":"rf32","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-46064-0"},{"key":"rf33","volume":"26","author":"He X. T.","journal-title":"J. Phys. A: Math. Gen."},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543043"},{"key":"rf35","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0092042","volume-title":"Invariant Manifolds","author":"Hirsch M. W.","year":"1977"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.63.2887"},{"key":"rf37","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.72.189"},{"key":"rf38","unstructured":"T.\u00a0Kawata, Advances in Nonlinear Waves, ed. L.\u00a0Debnath (Cambridge University Press, Cambridge, 1984)\u00a0pp. 210\u2013225."},{"key":"rf39","first-page":"2159","volume":"15","author":"Lamb G. L.","journal-title":"J. Math. Phys."},{"key":"rf40","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160210503"},{"key":"rf41","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0312(199611)49:11<1175::AID-CPA2>3.0.CO;2-9"},{"key":"rf42","doi-asserted-by":"publisher","DOI":"10.1007\/s003329900074"},{"key":"rf43","doi-asserted-by":"publisher","DOI":"10.1007\/s003329910005"},{"key":"rf44","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9590.00002"},{"key":"rf45","first-page":"101","volume":"111","author":"Li Y.","journal-title":"Stud. Appl. Math."},{"key":"rf46","volume-title":"Chaos in Partial Differential Equations","author":"Li Y.","year":"2004"},{"key":"rf47","doi-asserted-by":"publisher","DOI":"10.4310\/DPDE.2004.v1.n1.a4"},{"key":"rf48","doi-asserted-by":"publisher","DOI":"10.4310\/DPDE.2004.v1.n2.a4"},{"key":"rf49","doi-asserted-by":"publisher","DOI":"10.1023\/B:JODY.0000010062.09599.d8"},{"key":"rf50","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740401014X"},{"key":"rf51","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(96)00043-7"},{"key":"rf52","first-page":"248","volume":"38","author":"Manakov S. V.","journal-title":"Soviet Phys. JETP"},{"key":"rf53","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-00922-2"},{"key":"rf54","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160290203"},{"key":"rf55","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160340204"},{"key":"rf56","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0436-2_2"},{"key":"rf58","first-page":"1","volume":"12","author":"Melnikov V. K.","journal-title":"Trans. Moscow Math. Soc."},{"key":"rf59","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.41.265"},{"key":"rf60","doi-asserted-by":"publisher","DOI":"10.1017\/S0022377800020249"},{"key":"rf62","volume-title":"Nonlinear Optics","author":"Newell A. C.","year":"1992"},{"key":"rf63","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511606359"},{"key":"rf64","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/32\/36\/305"},{"key":"rf65","first-page":"279","volume":"16","author":"Rothos V. M.","journal-title":"Dyn. Syst."},{"key":"rf66","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402005431"},{"key":"rf67","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(98)00317-0"},{"key":"rf68","doi-asserted-by":"publisher","DOI":"10.1002\/0471213748"},{"key":"rf69","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(87)90227-2"},{"key":"rf70","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0312(200003)53:3<283::AID-CPA1>3.0.CO;2-2"},{"key":"rf71","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(96)00090-4"},{"key":"rf72","first-page":"1865","volume":"46","author":"Wadati M.","journal-title":"J. Phys. Soc. Jpn."},{"key":"rf73","first-page":"1386","volume":"23","author":"Wahlquist H. D.","journal-title":"Phys. Rev. Lett."},{"key":"rf74","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1042-9"},{"key":"rf75","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(00)00021-X"},{"key":"rf76","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(03)00446-6"},{"key":"rf77","first-page":"62","volume":"34","author":"Zakharov V. E.","journal-title":"Soviet Phys. JEPT"},{"key":"rf78","doi-asserted-by":"publisher","DOI":"10.1007\/BF01075696"},{"key":"rf79","volume-title":"The Theory of Solitons: The Inverse Problem Method","author":"Zakharov V. E.","year":"1980"},{"key":"rf80","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0312(200010)53:10<1222::AID-CPA2>3.0.CO;2-F"},{"key":"rf81","doi-asserted-by":"publisher","DOI":"10.1080\/02681119608806219"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127406016471","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T11:03:41Z","timestamp":1565175821000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127406016471"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10]]},"references-count":79,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,10]]}},"alternative-id":["10.1142\/S0218127406016471"],"URL":"https:\/\/doi.org\/10.1142\/s0218127406016471","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,10]]}}}