{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:39:24Z","timestamp":1772293164423,"version":"3.50.1"},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,5,4]],"date-time":"2012-05-04T00:00:00Z","timestamp":1336089600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rev Mat Complut"],"published-print":{"date-parts":[[2013,7]]},"DOI":"10.1007\/s13163-012-0097-8","type":"journal-article","created":{"date-parts":[[2012,5,3]],"date-time":"2012-05-03T06:25:01Z","timestamp":1336026301000},"page":"409-426","source":"Crossref","is-referenced-by-count":13,"title":["Convergence of a numerical scheme for a coupled Schr\u00f6dinger\u2013KdV system"],"prefix":"10.1007","volume":"26","author":[{"given":"Paulo","family":"Amorim","sequence":"first","affiliation":[]},{"given":"M\u00e1rio","family":"Figueira","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,5,4]]},"reference":[{"issue":"2","key":"97_CR1","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1006\/jfan.1998.3257","volume":"158","author":"D. Bekiranov","year":"1998","unstructured":"Bekiranov, D., Ogawa, T., Ponce, G.: Interaction equations for short and long dispersive waves. J.\u00a0Funct. Anal. 158(2), 357\u2013388 (1998)","journal-title":"J.\u00a0Funct. Anal."},{"key":"97_CR2","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1002\/sapm197756181","volume":"56","author":"D.J. Benney","year":"1977","unstructured":"Benney, D.J.: A general theory for interactions between short and long waves. Stud. Appl. Math. 56, 81\u201394 (1977)","journal-title":"Stud. Appl. Math."},{"issue":"2","key":"97_CR3","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/BF01896020","volume":"3","author":"J. Bourgain","year":"1993","unstructured":"Bourgain, J.: Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schr\u00f6dinger equations. Geom. Funct. Anal. 3(2), 107\u2013156 (1993)","journal-title":"Geom. Funct. Anal."},{"issue":"9","key":"97_CR4","doi-asserted-by":"crossref","first-page":"4089","DOI":"10.1090\/S0002-9947-07-04239-0","volume":"359","author":"A.J. Corcho","year":"2007","unstructured":"Corcho, A.J., Linares, F.: Well-posedness for the Schr\u00f6dinger\u2013Korteweg\u2013de Vries system. Trans. Am. Math. Soc. 359(9), 4089\u20134106 (2007)","journal-title":"Trans. Am. Math. Soc."},{"key":"97_CR5","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1007\/s11069-010-9535-4","volume":"57","author":"W. Craig","year":"2011","unstructured":"Craig, W., Guyenne, Ph., Sulem, C.: Coupling between internal and surface waves. Nat. Hazards 57, 617\u2013642 (2011)","journal-title":"Nat. Hazards"},{"issue":"8","key":"97_CR6","doi-asserted-by":"crossref","first-page":"2686","DOI":"10.1016\/j.na.2010.06.049","volume":"73","author":"J.-P. Dias","year":"2010","unstructured":"Dias, J.-P., Figueira, M., Oliveira, F.: Well-posedness and existence of bound states for a coupled Schr\u00f6dinger\u2013gKdV system. Nonlinear Anal. 73(8), 2686\u20132698 (2010)","journal-title":"Nonlinear Anal."},{"issue":"19\u201320","key":"97_CR7","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1016\/j.crma.2010.09.018","volume":"384","author":"J.-P. Dias","year":"2010","unstructured":"Dias, J.-P., Figueira, M., Oliveira, F.: Existence of bound states for the coupled Schr\u00f6dinger\u2013gKdV system with cubic nonlinearity. C. R. Math. Acad. Sci. Paris 384(19\u201320), 1079\u20131082 (2010)","journal-title":"C. R. Math. Acad. Sci. Paris"},{"key":"97_CR8","first-page":"93","volume-title":"Adv. Math. Suppl. Stud.","author":"T. Kato","year":"1983","unstructured":"Kato, T.: On the Cauchy problem for the (generalized) Korteweg\u2013de Vries equation. Studies in applied mathematics. In: Adv. Math. Suppl. Stud., vol.\u00a08, pp.\u00a093\u2013128. Academic Press, New York (1983)"},{"key":"97_CR9","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1143\/JPSJ.39.1379","volume":"39","author":"T. Kawahara","year":"1975","unstructured":"Kawahara, T., Sugimoto, N., Kakutani, T.: Nonlinear interaction between short and long capillary-gravity waves. J. Phys. Soc. Jpn. 39, 1379\u20131386 (1975)","journal-title":"J. Phys. Soc. Jpn."},{"issue":"1","key":"97_CR10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1215\/S0012-7094-93-07101-3","volume":"71","author":"C.E. Kenig","year":"1993","unstructured":"Kenig, C.E., Ponce, G., Vega, L.: The Cauchy problem for the Korteweg\u2013de Vries equation in Sobolev spaces of negative indices. Duke Math. J. 71(1), 1\u201321 (1993)","journal-title":"Duke Math. J."},{"issue":"2","key":"97_CR11","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1090\/S0894-0347-96-00200-7","volume":"9","author":"C.E. Kenig","year":"1996","unstructured":"Kenig, C.E., Ponce, G., Vega, L.: A bilinear estimate with applications to the KdV equation. J. Am. Math. Soc. 9(2), 573\u2013603 (1996)","journal-title":"J. Am. Math. Soc."},{"key":"97_CR12","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1103\/PhysRevLett.33.148","volume":"33","author":"K. Nishikawa","year":"1974","unstructured":"Nishikawa, K., Hojo, H., Mima, K., Ikezi, H.: Coupled nonlinear electron-plasma and ion acoustic waves. Phys. Rev. Lett. 33, 148\u2013151 (1974)","journal-title":"Phys. Rev. Lett."},{"key":"97_CR13","first-page":"513","volume-title":"GAKUTO Internat. Ser. Math. Sci. Appl.","author":"M. Tsutsumi","year":"1993","unstructured":"Tsutsumi, M.: Well-posedness of the Cauchy problem for a coupled Schr\u00f6dinger\u2013KdV equation. Nonlinear mathematical problems in industry, II. In: GAKUTO Internat. Ser. Math. Sci. Appl., vol.\u00a02, pp.\u00a0513\u2013528, Iwaki, 1992 (1993)"},{"key":"97_CR14","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1143\/PTP.62.370","volume":"62","author":"N. Yajima","year":"1979","unstructured":"Yajima, N., Satsuma, J.: Soliton solutions in a diatomic lattice system. Prog. Theor. Phys. 62, 370\u2013378 (1979)","journal-title":"Prog. Theor. Phys."}],"container-title":["Revista Matem\u00e1tica Complutense"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13163-012-0097-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13163-012-0097-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13163-012-0097-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T14:42:49Z","timestamp":1559486569000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13163-012-0097-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5,4]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,7]]}},"alternative-id":["97"],"URL":"https:\/\/doi.org\/10.1007\/s13163-012-0097-8","relation":{},"ISSN":["1139-1138","1988-2807"],"issn-type":[{"value":"1139-1138","type":"print"},{"value":"1988-2807","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5,4]]}}}