{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T23:16:11Z","timestamp":1648595771116},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2012,12,1]],"date-time":"2012-12-01T00:00:00Z","timestamp":1354320000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2012,12]]},"DOI":"10.1007\/s11424-012-9297-z","type":"journal-article","created":{"date-parts":[[2012,12,28]],"date-time":"2012-12-28T07:47:58Z","timestamp":1356680878000},"page":"1234-1248","source":"Crossref","is-referenced-by-count":0,"title":["Automated derivation of the conservation laws for nonlinear differential-difference equations"],"prefix":"10.1007","volume":"25","author":[{"given":"Jiaofeng","family":"Zhu","sequence":"first","affiliation":[]},{"given":"Yinping","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,12,29]]},"reference":[{"key":"9297_CR1","volume-title":"Symbolic computation of conserved densities and fluxes for nonlinear system of differential-difference equations","author":"H. Eklund","year":"2003","unstructured":"H. Eklund, Symbolic computation of conserved densities and fluxes for nonlinear system of differential-difference equations, Master of Science Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, 2003."},{"key":"9297_CR2","volume-title":"Direct Methods and Symbolic Software for Conservation Laws of Nonlinear Equations, Advances in Nonlinear Waves and Symbolic Computation","author":"W. Hereman","year":"2008","unstructured":"W. Hereman, P. J. Adams, H. L. Eklund, M. S. Hickman, and B. M. Herbst, Direct Methods and Symbolic Software for Conservation Laws of Nonlinear Equations, Advances in Nonlinear Waves and Symbolic Computation (ed. by Z. Yan), Nova Science Publishers, New York, 2008."},{"key":"9297_CR3","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1016\/j.amc.2005.04.049","volume":"173","author":"R. X. Yao","year":"2006","unstructured":"R. X. Yao and Z. B. Li, CONSLAW: A Maple package to construct the conservation laws for nonlinear evolution equations, Appl. Math. Comput., 2006, 173: 616\u2013635.","journal-title":"Appl. Math. Comput."},{"key":"9297_CR4","series-title":"London Mathematical Society Lecture Note Series","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511623998","volume-title":"Soliton, Nonlinear Evolution Equations and Inverse Scattering","author":"M. J. Ablowitz","year":"1991","unstructured":"M. J. Ablowitz and P. A. Clarkson, Soliton, Nonlinear Evolution Equations and Inverse Scattering, London Mathematical Society Lecture Note Series 149, Cambridge University Press, Cambridge, 1991."},{"key":"9297_CR5","first-page":"51","volume-title":"Contemp. Math.","author":"I. M. Anderson","year":"1992","unstructured":"I. M. Anderson, Introduction to the variational bicomplex, Contemp. Math., AMS, Providence, Rhode Island, 1992, 132: 51\u201373."},{"key":"9297_CR6","volume-title":"The Variational Bicomplex","author":"I. M. Anderson","year":"2004","unstructured":"I. M. Anderson, The Variational Bicomplex, Department of Mathematics, Utah State University, Logan, Utah, 2004."},{"key":"9297_CR7","volume-title":"Symmetries and Conservation Laws for Differential Equations of Mathematical Physics","author":"I. S. Krasil\u2019shchik","year":"1998","unstructured":"I. S. Krasil\u2019shchik and A. M. Vinogradov, Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, AMS, Providence, Rhode Island, 1998."},{"key":"9297_CR8","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4350-2","volume-title":"Applications of Lie Groups to Differential Equations","author":"P. J. Olver","year":"1993","unstructured":"P. J. Olver, Applications of Lie Groups to Differential Equations, 2nd edition, Graduate Texts in Mathematics 107, Springer Verlag, New York, 1993.","edition":"2nd edition"},{"key":"9297_CR9","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1017\/S095679250100465X","volume":"13","author":"S. C. Anco","year":"2002","unstructured":"S. C. Anco and G. Bluman, Direct construction method for conservation laws of partial differential equations. Part I: Examples of conservation law classifications, Europ. J. Appl. Math, 2002, 13: 545\u2013566.","journal-title":"Europ. J. Appl. Math"},{"key":"9297_CR10","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1017\/S0956792501004661","volume":"13","author":"S. C. Anco","year":"2002","unstructured":"S. C. Anco and G. Bluman, Direct construction method for conservation laws of partial differential equations: Part II: General treatment, Europ. J. Appl. Math, 2002, 13: 567\u2013585.","journal-title":"Europ. J. Appl. Math"},{"key":"9297_CR11","series-title":"Applied Mathematical Sciences","volume-title":"Symmetry and Integration Methods for Differential Equations","author":"G. W. Bluman","year":"2002","unstructured":"G. W. Bluman and S. C. Anco, Symmetry and Integration Methods for Differential Equations, Applied Mathematical Sciences 154, Springer-Verlag, Berlin, 2002."},{"key":"9297_CR12","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.cpc.2006.08.001","volume":"176","author":"A. F. Cheviakov","year":"2007","unstructured":"A. F. Cheviakov, GeM software package for computation of symmetries and conservation laws of differential equations, Comp. Phys. Comm., 2007, 176: 48\u201361.","journal-title":"Comp. Phys. Comm."},{"key":"9297_CR13","first-page":"377","volume":"2","author":"A. B. Shabat","year":"1991","unstructured":"A. B. Shabat and R. I. Yamilov, Symmetries of the nonlinear chains, Leningrad Math. J., 1991, 2: 377\u2013400.","journal-title":"Leningrad Math. J."},{"key":"9297_CR14","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/S0375-9601(99)00087-0","volume":"254","author":"V. E. Adler","year":"1999","unstructured":"V. E. Adler, S. I. Svinolupov, and R. I. Yamilov, Multi-component Volterra and Toda type integrable equations, Phys. Lett. A, 1999, 254: 24\u201336.","journal-title":"Phys. Lett. A"},{"key":"9297_CR15","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/S0960-0779(01)00238-7","volume":"14","author":"D. J. Zhang","year":"2002","unstructured":"D. J. Zhang and D. Y. Chen, The conservation laws of some discrete soliton systems, Chaos, Solitons & Fractals, 2002, 14: 573\u2013579.","journal-title":"Chaos, Solitons & Fractals"},{"key":"9297_CR16","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1006\/jsco.1998.0250","volume":"27","author":"T. Wolf","year":"1999","unstructured":"T. Wolf, A. Brand, and M. Mohammadzadeh, Computer algebra algorithms and routines for the computation of conservation laws and fixing of gauge in differential expressions, J. Symb. Comp., 1999, 27: 221\u2013238.","journal-title":"J. Symb. Comp."},{"key":"9297_CR17","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/S0375-9601(97)00750-0","volume":"236","author":"G\u00f6ktas","year":"1997","unstructured":"\u00dc. G\u00f6ktas, W. H Hereman, and G. Erdmann, Computation of conserved densities for systems of nonlinear differential-difference equations, Phys. Lett. A, 1997, 236: 30\u201338.","journal-title":"Phys. Lett. A"},{"key":"9297_CR18","volume-title":"The Basic Principle of Mechanical Geometry Theorem Proving","author":"W. T. Wu","year":"1984","unstructured":"W. T. Wu, The Basic Principle of Mechanical Geometry Theorem Proving, Science Press, Beijing, 1984."},{"key":"9297_CR19","volume-title":"Mathematics Mechanization","author":"W. T. Wu","year":"2000","unstructured":"W. T. Wu, Mathematics Mechanization, Science Press-Kluwer Academic Publishers, Beijing-Dordrecht-Boston-London, 2000."},{"issue":"4","key":"9297_CR20","first-page":"289","volume":"2","author":"W. T. Wu","year":"1989","unstructured":"W. T. Wu, On the foundation of algebraic differential geometry, Syst. Sci. Math Sci., 1989, 2(4): 289\u2013312.","journal-title":"Syst. Sci. Math Sci."},{"key":"9297_CR21","first-page":"331","volume":"4","author":"C. L. Temuer","year":"2010","unstructured":"C. L. Temuer and Y. S. Bai, A new algorithmic theory for determining and classifying classical and non-classical symmetries of partial differential equations, Science China Press, 2010, 4: 331\u2013348.","journal-title":"Science China Press"},{"key":"9297_CR22","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s10665-009-9344-5","volume":"66","author":"C. L. Temuer","year":"2010","unstructured":"C. L. Temuer and J. Pang, An algorithm for the complete symmetry classification of differential equations based on Wu\u2019s method, J. Eng. Math, 2010, 66: 181\u2013199.","journal-title":"J. Eng. Math"},{"key":"9297_CR23","doi-asserted-by":"crossref","first-page":"1694","DOI":"10.1016\/j.chaos.2006.03.023","volume":"33","author":"Z. H. Yang","year":"2007","unstructured":"Z. H. Yang and Y. C. Hon, A generalized coth-function method for exact solution of differentialdifference equation, Chaos, Solitons & Fractals, 2007, 33: 1694\u20131702.","journal-title":"Chaos, Solitons & Fractals"},{"key":"9297_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-96585-2","volume-title":"Theory of Nonlinear Lattices","author":"M. Toda","year":"1981","unstructured":"M. Toda, Theory of Nonlinear Lattices, Springer-Verlag, Berlin, 1981."},{"key":"9297_CR25","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/0378-4754(93)90069-7","volume":"35","author":"T. R. Taha","year":"1993","unstructured":"T. R. Taha, A differential-difference equation for a KdV-MKdV equation, Maths. Comput. in Simul, 1993, 35: 509\u2013512.","journal-title":"Maths. Comput. in Simul"},{"key":"9297_CR26","doi-asserted-by":"crossref","first-page":"L883","DOI":"10.1088\/0305-4470\/25\/14\/004","volume":"25","author":"A. Ramani","year":"1992","unstructured":"A. Ramani, B. Grammaticos, and K.M. Tamizhmani, An integrability test for differential-difference systems, Phys. A, 1992, 25: L883\u2013L886.","journal-title":"Phys. A"},{"key":"9297_CR27","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1002\/sapm1976553213","volume":"55","author":"M. J. Ablowitz","year":"1976","unstructured":"M. J. Ablowitz and J. F. Ladik, A nonlinear difference scheme and inverse scattering, Stud. Appl. Math, 1976, 55: 213\u2013229.","journal-title":"Stud. Appl. Math"},{"key":"9297_CR28","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1016\/j.camwa.2009.01.008","volume":"57","author":"X. L. Yong","year":"2009","unstructured":"X. L. Yong, X. Zeng, Z. Y. Zhang, and Y. F. Chen, Symbolic computation of Jacobi elliptic function solutions to nonlinear differential-difference equations, Computers and Mathematics with Applications, 2009, 57: 1107\u20131114.","journal-title":"Computers and Mathematics with Applications"},{"key":"9297_CR29","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1143\/PTPS.59.36","volume":"59","author":"M. Wadati","year":"1976","unstructured":"M. Wadati, Transformation theories for nonlinear discrete systems, Prog. Theor. Phys. Suppl., 1976, 59: 36\u201363.","journal-title":"Prog. Theor. Phys. Suppl."},{"key":"9297_CR30","unstructured":"R. Hirota and M. Iwao, Time-Discretization of Soliton Equations\/\/SIDE III-symmetries and integrability of difference equations, CRM Proceedings & Lecture Notes, 2000, 25."},{"key":"9297_CR31","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.cpc.2004.07.002","volume":"162","author":"D. Baldwin","year":"2004","unstructured":"D. Baldwin, \u00dc. G\u00f6ktas, and W. Hereman, Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations, Comput. Phys. Comm., 2004, 162: 203\u2013217.","journal-title":"Comput. Phys. Comm."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-012-9297-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11424-012-9297-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-012-9297-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,7]],"date-time":"2019-07-07T17:19:20Z","timestamp":1562519960000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11424-012-9297-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":31,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["9297"],"URL":"https:\/\/doi.org\/10.1007\/s11424-012-9297-z","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}