Variational problem, Lagrangian and $\mu$-conservation law of the generalized Rosenau-type equation

[1] G. Cicogna and G. Gaeta, Noether theorem for µ-symmetries, J. Phys. A: Math. Theor., 40 (2007), p. 11899.
[2] A. Esfahani, Solitary wave solutions for generalized Rosenau-KdV equation, Commun. Theor. Phys., 55
(2011), p. 396.
[3] G. Gaeta and P. Morando, On the geometry of lambda-symmetries and PDE reduction, J. Phys. A: Math.
Gen., 37 (2004), p. 6955.
[4] D. J. Korteweg and G. de Vries, On the change of form of long waves advancing in a rectangular canal,
and on a new type of long stationary waves, Phil. Mag., 39 (1895), pp. 422–443.
[5] C. Muriel, J. L. Romero, and P. J. Olver, Variational C∞-symmetries and Euler-Lagrange equations,
J. Differential Equations, 222 (2006), pp. 164–184.
[6] P. J. Olver, Applications of Lie groups to differential equations, vol. 107 of Graduate Texts in Mathematics,
Springer-Verlag, New York, 1986.
[7] X. Pan and L. Zhang, On the convergence of a conservative numerical scheme for the usual Rosenau-RLW
equation, Appl. Math. Model., 36 (2012), pp. 3371–3378.
[8] D. H. Peregrine, Calculations of the development of an undular bore, J. Fluid Mech., 25 (1966), pp. 321–330.
[9] P. Rosenau, A quasi-continuous description of a nonlinear transmission line, Phys. Scr., 34 (1986), p. 827.
[10] P. Rosenau, Dynamics of dense discrete systems: High order effects, Prog. Theor. Phys., 79 (1988), pp. 1028–
1042.
[11] J.-M. Zuo, Y.-M. Zhang, T.-D. Zhang, and F. Chang, A new conservative difference scheme for the
general Rosenau-RLW equation, Bound. Value Probl., (2010), pp. Art. ID 516260, 13.