{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T17:47:29Z","timestamp":1773683249843,"version":"3.50.1"},"reference-count":35,"publisher":"Elsevier BV","issue":"2-3","license":[{"start":{"date-parts":[[2001,2,1]],"date-time":"2001-02-01T00:00:00Z","timestamp":980985600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Numerical Mathematics"],"published-print":{"date-parts":[[2001,2]]},"DOI":"10.1016\/s0168-9274(99)00148-8","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T12:56:43Z","timestamp":1027601803000},"page":"197-217","source":"Crossref","is-referenced-by-count":16,"title":["Error propagation in the numerical integration of solitary waves. The regularized long wave equation"],"prefix":"10.1016","volume":"36","author":[{"given":"A.","family":"Ara\u00fajo","sequence":"first","affiliation":[]},{"given":"A.","family":"Dur\u00e1n","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0168-9274(99)00148-8_BIB001","series-title":"Mathematical Methods of Classical Mechanics","author":"Arnold","year":"1989"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB002","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1098\/rspa.1972.0074","article-title":"The stability of solitary waves","volume":"328","author":"Benjamin","year":"1972","journal-title":"Proc. R. Soc. London Ser. A"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB003","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1098\/rsta.1972.0032","article-title":"Model equations for long waves in nonlinear dispersive systems","volume":"272","author":"Benjamin","year":"1972","journal-title":"Philos. Trans. R. Soc. London Ser. A"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB004","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1007\/BF02430641","article-title":"On the stability of solitary wave solutions of model equations for long waves","volume":"4","author":"Bona","year":"1994","journal-title":"J. Nonlinear Sci."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB005","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0168-9274(95)00046-W","article-title":"Accurate long-term integration of dynamical systems","volume":"18","author":"Calvo","year":"1995","journal-title":"Appl. Numer. Math."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB006","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1137\/0914057","article-title":"The development of variable-step symplectic integrators with application to the two-body problem","volume":"14","author":"Calvo","year":"1993","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB007","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1137\/S0036142995281152","article-title":"Error growth in the numerical integration of periodic orbits, with application to Hamiltonian and reversible systems","volume":"34","author":"Cano","year":"1997","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB008","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/0165-2125(94)90003-5","article-title":"Hamiltonian long-wave approximations to the water-wave problem","volume":"19","author":"Craig","year":"1994","journal-title":"Wave Motion"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB009","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1007\/s002110050247","article-title":"Accuracy and conservation properties in numerical integration: the case of the Korteweg\u2013de Vries equation","volume":"75","author":"Frutos","year":"1997","journal-title":"Numer. Math."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB010","series-title":"Solitons. An Introduction","author":"Drazin","year":"1990"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB011","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1088\/0951-7715\/11\/6\/008","article-title":"The numerical integration of relative equilibrium solutions. Geometric theory","volume":"11","author":"Dur\u00e1n","year":"1998","journal-title":"Nonlinearity"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB012","unstructured":"A. Dur\u00e1n, J.M. Sanz-Serna, The numerical integration of relative equilibrium solutions. The nonlinear Schr\u00f6dinger equation, to appear in IMA J. Numer. Anal"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB013","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/0021-9991(77)90088-2","article-title":"Numerical study of the regularized long-wave equation II: interaction of solitary waves","volume":"23","author":"Eilbeck","year":"1977","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB014","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/BF01003559","article-title":"The rate of error growth in Hamiltonian conserving integrators","volume":"46","author":"Estep","year":"1995","journal-title":"Z. Angew. Math. Phys."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB015","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/0021-9991(90)90047-5","article-title":"Solitary waves of the regularised longwave equation","volume":"91","author":"Gardner","year":"1990","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB016","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/0021-9991(92)90054-3","article-title":"Solitary waves of the equal width wave equation","volume":"101","author":"Gardner","year":"1992","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB017","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0167-2789(92)90246-J","article-title":"Invariants and numerical methods for ODEs","volume":"60","author":"Gear","year":"1990","journal-title":"Phys. D"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB018","series-title":"Solving Ordinary Differential Equations I, Nonstiff Problems","author":"Hairer","year":"1993"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB019","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/0021-9991(88)90132-5","article-title":"Hamiltonian-conserving discrete canonical equations based on variational difference quotients","volume":"77","author":"Itoh","year":"1988","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB020","series-title":"Introduction to Mechanics and Symmetry","author":"Marsden","year":"1994"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB021","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1002\/(SICI)1097-0312(199604)49:4<399::AID-CPA4>3.0.CO;2-7","article-title":"Asymptotic stability of solitary waves for the regularized long-wave equation","volume":"49","author":"Miller","year":"1996","journal-title":"Comm. Pure Appl. Math."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB022","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/0167-2789(84)90014-9","article-title":"Scattering of regularized-long-wave solitary waves","volume":"11","author":"Morrison","year":"1984","journal-title":"Phys. D"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB023","series-title":"Applications of Lie Groups to Differential Equations","author":"Olver","year":"1993"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB024","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1017\/S0305004100055572","article-title":"Euler operators and conservation laws of the BBM equation","volume":"85","author":"Olver","year":"1979","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB025","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/0021-9991(90)90228-S","article-title":"Pseudospectral solution of nonlinear Schr\u00f6dinger equations","volume":"87","author":"Pathria","year":"1990","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB026","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/BF02101705","article-title":"Asymptotic stability of solitary waves","volume":"164","author":"Pego","year":"1994","journal-title":"Comm. Math. Phys."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB027","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1017\/S0022112066001678","article-title":"Calculations of the development of an undular bore","volume":"25","author":"Peregrine","year":"1996","journal-title":"J. Fluid Mech."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB028","series-title":"The State of the Art in Numerical Analysis","first-page":"121","article-title":"Geometric integration","author":"Sanz-Serna","year":"1997"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB029","series-title":"Numerical Hamiltonian Problems","author":"Sanz-Serna","year":"1994"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB030","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0377-0427(91)90024-E","article-title":"Fourier pseudospectral solution of the regularised long wave equation","volume":"36","author":"Sloan","year":"1991","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB031","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02238234","article-title":"Variable steps for reversible integration methods","volume":"55","author":"Stoffer","year":"1995","journal-title":"Computing"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB032","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/0021-9991(78)90038-4","article-title":"Numerical solution of a nonlinear Klein\u2013Gordon equation","volume":"28","author":"Strauss","year":"1978","journal-title":"J. Comput. Phys."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB033","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1137\/0516034","article-title":"Modulational stability of ground states of nonlinear Schr\u00f6dinger equations","volume":"16","author":"Weinstein","year":"1985","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/S0168-9274(99)00148-8_BIB034","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1080\/03605308708820522","article-title":"Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation","volume":"12","author":"Weinstein","year":"1987","journal-title":"Comm. Partial Differential Equations"},{"key":"10.1016\/S0168-9274(99)00148-8_BIB035","series-title":"Linear and Nonlinear Waves","author":"Whitham","year":"1974"}],"container-title":["Applied Numerical Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0168927499001488?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0168927499001488?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T09:01:01Z","timestamp":1556182861000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0168927499001488"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,2]]},"references-count":35,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2001,2]]}},"alternative-id":["S0168927499001488"],"URL":"https:\/\/doi.org\/10.1016\/s0168-9274(99)00148-8","relation":{},"ISSN":["0168-9274"],"issn-type":[{"value":"0168-9274","type":"print"}],"subject":[],"published":{"date-parts":[[2001,2]]}}}