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  • 1. Anco, S.
    et al.
    Ibragimov, Nail
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Imamutdinova, K.V.
    Karimova, E.N.
    Solutions of gasdynamic equations associated with classical and new conservation laws2015In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 268, p. 52-58Article in journal (Refereed)
    Abstract [en]

    Exact solutions of the one-dimensional gasdynamic equations are constructed by applying the method of conservation laws to all point-wise conserved vectors of the equations under consideration. © 2015 Elsevier Inc.

  • 2.
    Ibragimov, Nail H.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Comments on the paper "Conservation laws of the (2+1)-dimensional KP equation and Burgers equation with variable coefficients and cross terms" by Li-Hua Zhang2014In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 226, p. 1-2Article in journal (Refereed)
    Abstract [en]

    The recent paper mentioned in the title contains a confusing statement on computing conservation laws corresponding to symmetries of nonlinearly self-adjoint differential equations. The present brief article contains clarifying comments.

  • 3.
    Ibragimov, Nail H.
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
    Cantoni, Antonio
    Self-adjointness of a generalized Camassa-Holm equation2011In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 218, no 6, p. 2579-2583Article in journal (Refereed)
    Abstract [en]

    It is well known that the Camassa-Holm equation possesses numerous remarkable properties characteristic for KdV type equations. In this paper we show that it shares one more property with the KdV equation. Namely, it is shown in [1,2] that the KdV and the modified KdV equations are self-adjoint. Starting from the generalization [3] of the Camassa-Holm equation [4], we prove that the Camassa-Holm equation is self-adjoint. This property is important, e.g. for constructing conservation laws associated with symmetries of the equation in question. Accordingly, we construct conservation laws for the generalized Camassa-Holm equation using its symmetries.

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