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2014 | 12 | 8 | 541-553
Tytuł artykułu

Residual symmetries of the modified Korteweg-de Vries equation and its localization

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The residual symmetries of the famous modified Korteweg-de Vries (mKdV) equation are researched in this paper. The initial problem on the residual symmetry of the mKdV equation is researched. The residual symmetries for the mKdV equation are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries by means of enlarging the mKdV equations. One-parameter invariant subgroups and the invariant solutions for the extended system are listed. Eight types of similarity solutions and the reduction equations are demonstrated. It is noted that we researched the twofold residual symmetries by means of taking the mKdV equation as an example. Similarity solutions and the reduction equations are demonstrated for the extended mKdV equations related to the twofold residual symmetries.
Wydawca

Czasopismo
Rocznik
Tom
12
Numer
8
Strony
541-553
Opis fizyczny
Daty
wydano
2014-08-01
online
2014-07-20
Twórcy
autor
  • Department of Physics and Electronics, Shangrao Normal University, Shangrao, 334001, China, sryangjr@163.com
Bibliografia
  • [1] R. M. Miura, J. Math. Phys. 9, 1202 (1968) http://dx.doi.org/10.1063/1.1664700[Crossref]
  • [2] P. Olver, Applications of Lie Group to Differential Equations (Spring-Verlag, New York, 1986) http://dx.doi.org/10.1007/978-1-4684-0274-2[Crossref]
  • [3] G. W. Bluman, S. Kumei, Symmetries and Differential Equations (Spring-Verlag, New York, 1989) http://dx.doi.org/10.1007/978-1-4757-4307-4[Crossref]
  • [4] R. Conte, Phys. Lett. A 140, 383 (1989) http://dx.doi.org/10.1016/0375-9601(89)90072-8[Crossref]
  • [5] S. Y. Lou, Z. Naturforsch A 53, 251 (1998)
  • [6] S. Y. Lou, X. R. Hu, Y. Chen, J. Phys. A: Math. Theor. 45, 155209 (2012) http://dx.doi.org/10.1088/1751-8113/45/15/155209[Crossref]
  • [7] P. Liu, Z. L. Li, S. Y. Lou, Appl. Math. Mech. 31, 1383 (2010) http://dx.doi.org/10.1007/s10483-010-1370-6[Crossref]
  • [8] X. Lü, M. Peng, Commun. Nonlinear Sci. Numer. Simulat. 18, 2304 (2013) http://dx.doi.org/10.1016/j.cnsns.2012.11.006[Crossref]
  • [9] Z.J. Qiao, Commun. Math. Phys. 239, 309 (2003) http://dx.doi.org/10.1007/s00220-003-0880-y[Crossref]
  • [10] X. Lü, M. Peng, Chaos 23, 013122 (2013) http://dx.doi.org/10.1063/1.4790827[Crossref]
  • [11] S. M. Ikhdair, R. Sever, Centr. Eur. J. Phys. 8, 652 (2010) http://dx.doi.org/10.2478/s11534-009-0118-5[Crossref]
  • [12] B. Q. Zeng, G. Y. Xiong, S. Chen, W. Z. Wang, Appl. Phys. Lett. 90, 033112 (2007) http://dx.doi.org/10.1063/1.2428543[Crossref]
  • [13] Z. L. Li, Z. Naturforsch A 65, 649 (2010)
  • [14] P. Painlevé, Acta Math. 25, 1 (1902) http://dx.doi.org/10.1007/BF02419020[Crossref]
  • [15] A. Ramani, B. Grammaticos, T. Bountis, Phys. Rep. 180, 159 (1989) http://dx.doi.org/10.1016/0370-1573(89)90024-0[Crossref]
  • [16] J. Weiss, M. Tabor, G. Carnevale, J. Math. Phys. 24, 522 (1983) http://dx.doi.org/10.1063/1.525721[Crossref]
  • [17] Y. L. Zhao, Y. P. Liu, Z. B. Li, Chin. Phys. B 19, 030306 (2010) http://dx.doi.org/10.1088/1674-1056/19/3/030306[Crossref]
  • [18] P. Liu, Z. L. Li, Chin. Phys. B 22, 050204 (2013) http://dx.doi.org/10.1088/1674-1056/22/5/050204[Crossref]
  • [19] P. Liu, Z. L. Li, R. Z. Luo, Appl. Math. Comput. 219, 2149 (2012) http://dx.doi.org/10.1016/j.amc.2012.08.061[Crossref]
  • [20] P. Liu, P. K. Fu, Commun. Theor. Phys. 56, 5 (2011) http://dx.doi.org/10.1088/0253-6102/56/1/02[Crossref]
  • [21] P. L. Ndlovu, R. J. Moitsheki, Centr. Eur. J. Phys. 11, 984 (2013) http://dx.doi.org/10.2478/s11534-013-0306-1[Crossref]
  • [22] A. S. Fokas, J. Math. Phys. 21, 1318 (1980) http://dx.doi.org/10.1063/1.524581[Crossref]
  • [23] S. Y. Lou, X. B. Hu, Chin. Phys. Lett. 10, 577 (1993) http://dx.doi.org/10.1088/0256-307X/10/10/001[Crossref]
  • [24] W. X. Ma, Physica A 219, 467 (1995) http://dx.doi.org/10.1016/0378-4371(95)00161-Y[Crossref]
  • [25] M. Y. Balakhnev, Math. Notes 82, 448 (2007) http://dx.doi.org/10.1134/S0001434607090180[Crossref]
  • [26] X. Y. Jiao, S. Y. Lou, Chin. Phys. B 18, 3611 (2009) http://dx.doi.org/10.1088/1674-1056/18/9/001[Crossref]
  • [27] X. Z. Liu, J. Phys. A: Math. Theor. 43, 265203 (2010) http://dx.doi.org/10.1088/1751-8113/43/26/265203[Crossref]
  • [28] E. Yaşar, J. Math. Anal. Appl. 363, 174 (2010) http://dx.doi.org/10.1016/j.jmaa.2009.08.030[Crossref]
  • [29] X. P. Xin, Q. Miao, Y. Chen, Chin. Phys. B 23, 010203 (2014) http://dx.doi.org/10.1088/1674-1056/23/1/010203[Crossref]
  • [30] X. N. Gao, S. Y. Lou, X. Y. Tang, J. High Energy Phys. 5, 029 (2013)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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