2015, 2015(special): 304-311. doi: 10.3934/proc.2015.0304

An equation unifying both Camassa-Holm and Novikov equations

1. 

Centro de Matemática, Computação e Cognição, Universidade Federal do ABC - UFABC, Rua Santa Adélia, 166, Bairro Bangu, 09.210 -- 170, Santo André, SP, Brazil, Brazil

Received  September 2014 Revised  January 2015 Published  November 2015

In this paper we derive a new equation unifying the Camassa-Holm and Novikov equations invariant under the scaling transformation $(x,t,u)\mapsto(x,\lambda^{-b}t,\lambda u)$ and admitting a certain multiplier.
Citation: Priscila Leal da Silva, Igor Leite Freire. An equation unifying both Camassa-Holm and Novikov equations. Conference Publications, 2015, 2015 (special) : 304-311. doi: 10.3934/proc.2015.0304
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show all references

References:
[1]

Cambridge University Press, (1991). Google Scholar

[2]

Phys. Rev. Lett., 78, (1987), 2869-2873. Google Scholar

[3]

European J. Appl. Math., 13, (2002), 545-566. Google Scholar

[4]

European J. Appl. Math., 13, (2002), 566-585. Google Scholar

[5]

Philos. Trans. Roy. Soc. London, 272, (1972), 47-78. Google Scholar

[6]

Springer, New York, (2010). Google Scholar

[7]

Springer, New York, (2002). Google Scholar

[8]

Applied Mathematical Sciences, 81, Springer, New York, (1989). Google Scholar

[9]

Comp. Appl. Math., 33, (2014), 193-202. Google Scholar

[10]

Phys. Rev. Lett., 71 (1993),1661-1664. Google Scholar

[11]

Math. Comput. Modelling., 25, (1997), 195-212. Google Scholar

[12]

(2013) arXiv:1312.3992. Google Scholar

[13]

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, (2015), DOI: 10.5540/03.2015.003.01.0022. Google Scholar

[14]

in Interdisciplinary Topics in Applied Mathematics, Modelling and Computational Science. Springer Proceedings in Mathematics and Statistics, 117 (2015), 161-166, DOI: 10.1007/978-3-319-12307-3_23. Google Scholar

[15]

Theor. Math. Phys., 133, (2002), 1463-1474. Google Scholar

[16]

Phys. Rev. Lett., 87, (2001), 194501, 4pp. Google Scholar

[17]

Fluid Dynamics Research, 333 (2003), 73-95. Google Scholar

[18]

J. Phys. A: Math. Theor., 41, (2008), 372002, 10 pp. Google Scholar

[19]

J. Math. Phys., 12, (1971), 1548-1551. Google Scholar

[20]

Translated from the Russian Mathematics and its Applications (Soviet Series), D. Reidel Publishing Co., Dordrecht, (1985). Google Scholar

[21]

John Wiley and Sons, Chirchester (1999). Google Scholar

[22]

J. Math. Anal. Appl., 333, (2007), 311-328. Google Scholar

[23]

Appl. Math. Comp., 218, (2011), 2579-2583. Google Scholar

[24]

J. Phys. A: Math. Theor., 44, (2011) 432002, 8 pp. Google Scholar

[25]

Archives of ALGA, 7/8, (2011), 1-90. Google Scholar

[26]

Int. J. Theor. Phys., 46, (2007), 2658-2668. Google Scholar

[27]

J. Diff. Equ., 254, (2013), 961-982. Google Scholar

[28]

Phil. Mag., 39, (1895), 422-443. Google Scholar

[29]

J. Math. Phys., 11, (1970),952-960. Google Scholar

[30]

J. Math. Phys., 9, (1968), 1202-1204. Google Scholar

[31]

J. Math. Phys., 9, (1968) 1204-1209. Google Scholar

[32]

J. Phys. A: Math. Theor., 42, (2009) 342002, 14pp. Google Scholar

[33]

Math. Proc. Cambridge Phils. Soc., 85, (1979), 143-160. Google Scholar

[34]

Math. Proc. Camb. Phil. Soc., 94, (1983), 529-540. Google Scholar

[35]

Trans. Amer. Math. Soc., 277, (1983), 353-380. Google Scholar

[36]

Springer, New York, (1986). Google Scholar

[37]

J. Math. Phys., 46, (2005), 43502. Google Scholar

[38]

J. Phys. A, 41, (2008), 362002. Google Scholar

[39]

Phys. Lett. A, 374, (2010), 2210-2217. Google Scholar

[40]

Acta Appl. Math., 2, (1984), 21-78. Google Scholar

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