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Acta Physica Sinica, Volume. 69, Issue 1, 010203-1(2020)

The Boussinesq equation: Lax pair, Bäcklund transformation, symmetry group transformation and consistent Riccati expansion solvability

Ping Liu1、*, Heng-Rui Xu2, and Jian-Rong Yang3
Author Affiliations
  • 1School of Electronic and Information Engineering, University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan 528402, China
  • 2School of Physics, University of Electronic Science and Technology of China, Chengdu 610054, China
  • 3School of Physics and Electronic Information, Shangrao Normal University, Shangrao 334001, China
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    [1] Boussinesq J[J]. J. Math. Pures Appl., 17, 55(1872).

    [2] Ursell F[J]. Proc. Cambridge Philos. Soc., 49, 685(1953).

    [3] Daripa P[J]. J. Comput. Appl. Math., 100, 161(1998).

    [4] Guo B, Gao Z, Lin J[J]. Commun. Theor. Phys., 64, 589(2016).

    [5] Liu W[J]. Z. Naturforschung A, 64, 709(2009).

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    [7] Himonas A A, Mantzavinos D[J]. J. Differ. Equations, 258, 3107(2015).

    [8] Li S, Zhang W, Bu X[J]. J. Math. Anal. Appl., 449, 96(2017).

    [9] Weiss J[J]. J. Math. Phys., 24, 1405(1983).

    [10] Guo B X, Lin J[J]. Int. J. Mod. Phys. B, 30, 1640013(2013).

    [11] Guo B X, Gao Z J, Lin J[J]. Commun. Theor. Phys., 66, 589(2016).

    [12] Liu Y K, Li B[J]. Chin. J. Phys., 54, 718(2016).

    [13] Gao X N, Lou SY, Tang X Y[J]. J. High Energy Phys., 5, 029(2013).

    [14] Olver P J[J]. Applications of Lie Group to Differential Equations 2nd ed., 75-238(1993).

    [15] Liu P, Zeng B Q, Ren B[J]. Commun. Theor. Phys., 63, 413(2015).

    [16] Liu Y K, Li B[J]. Chin. Phys. Lett., 34, 010202(2017).

    [17] Liu P, Zeng B Q, Deng B B, Yang J R[J]. AIP Adv., 5, 087162(2015).

    [18] Liu P, Wang Y X, Ren B, Li J H[J]. Commun. Theor. Phys., 66, 595(2016).

    [19] Jiao X Y, Jia M, An H L[J]. Acta Phys. Sin., 68, 140201(2019).

    [20] Lou S Y[J]. Stud. Appl. Math., 134, 372(2015).

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    Ping Liu, Heng-Rui Xu, Jian-Rong Yang. The Boussinesq equation: Lax pair, Bäcklund transformation, symmetry group transformation and consistent Riccati expansion solvability[J]. Acta Physica Sinica, 2020, 69(1): 010203-1

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    Paper Information

    Received: Sep. 2, 2019

    Accepted: --

    Published Online: Nov. 4, 2020

    The Author Email:

    DOI:10.7498/aps.69.20191316

    Topics

    Nuclear physics
    Particles and fields
    Particle and nuclear astrophysics and cosmology