Study on a General Hopf Hierarchy
By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.For the first order Hopf equation,there exist infinitely many symmetries which can be...
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| Published in | Communications in theoretical physics Vol. 65; no. 4; pp. 393 - 396 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.04.2016
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0253-6102 1572-9494 |
| DOI | 10.1088/0253-6102/65/4/393 |
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| Abstract | By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.For the first order Hopf equation,there exist infinitely many symmetries which can be expressed by means of an arbitrary function in arbitrary dimensions.The general solution of the first order Hopf equation is obtained via hodograph transformation.For the second order Hopf equation,the Hopf-diffusion equation,there are five sets of infinitely many symmetries.Especially,there exist a set of primary branch symmetry with which contains an arbitrary solution of the usual linear diffusion equation.Some special implicit exact group invariant solutions of the Hopf-diffusion equation are also given. |
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| AbstractList | By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.For the first order Hopf equation,there exist infinitely many symmetries which can be expressed by means of an arbitrary function in arbitrary dimensions.The general solution of the first order Hopf equation is obtained via hodograph transformation.For the second order Hopf equation,the Hopf-diffusion equation,there are five sets of infinitely many symmetries.Especially,there exist a set of primary branch symmetry with which contains an arbitrary solution of the usual linear diffusion equation.Some special implicit exact group invariant solutions of the Hopf-diffusion equation are also given. |
| Author | 崔敏婕 楼森岳 |
| AuthorAffiliation | Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China Ningbo Collabrative Innovation Center of Nonlinear Harzard System of Ocean and Atmosphere and Faculty of Science, Ningbo University, Ningbo 315211, China |
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| Cites_doi | 10.1063/1.523393 10.1016/0167-2789(81)90004-X 10.1016/j.aml.2015.06.011 10.1016/0362-546X(79)90052-X 10.1137/1.9781611970883 10.1063/1.1664701 10.1002/cpa.3160030302 10.1063/1.530509 10.1063/1.530872 10.1143/PTP.70.1508 10.1088/0305-4470/26/17/043 |
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| Notes | Min-Jie Cui, Sen-Yue Lou （1Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China ;2 Ningbo Collabrative Innovation Center of Nonlinear Harzard System of Ocean and Atmosphere and Faculty of Science Ningbo University, Ningbo 315211, China） Hopf hierarchy symmetries hereditary operator exact solutions nonlinear diffusion equations 11-2592/O3 By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.For the first order Hopf equation,there exist infinitely many symmetries which can be expressed by means of an arbitrary function in arbitrary dimensions.The general solution of the first order Hopf equation is obtained via hodograph transformation.For the second order Hopf equation,the Hopf-diffusion equation,there are five sets of infinitely many symmetries.Especially,there exist a set of primary branch symmetry with which contains an arbitrary solution of the usual linear diffusion equation.Some special implicit exact group invariant solutions of the Hopf-diffusion equation are also given. ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
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| References | 12 Polyanin A.D. (15) 2002 Lou S.Y. (5) 1993; 26 14 Lou S.Y. (11) Li Y.S. (13) 1990; 23 Olver P.J. (7) 1986 1 2 3 4 6 8 9 10 |
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| Snippet | By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf... By using a general symmetry theory related to invariant functions, strong symmetry operators and hereditary operators, we find a general integrable hopf... |
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| SubjectTerms | Diffusion Hierarchies Hodographs Hopf方程 Invariants Lax对 Mathematical analysis Operators Symmetry Transformations 对称算子 广义对称 扩散方程 无穷多 结构 遗传算子 |
| Title | Study on a General Hopf Hierarchy |
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