Galilei-invariant higher-order equations of burgers and korteweg-de vries types

G. B. Whitham,Linear and Nonlinear Waves, Wiley, New York 1974. V. A. Krasil’nikov and V. A. Krylov,Introduction to Physical Acoustics [in Russian], Nauka, Moscow 1984. O. V. Rudenko and S. I. Soluyan,Theoretical Foundations of Nonlinear Acoustics [in Russian], Nauka, Moscow 1975. P. L. Sachdev,Nonlinear Diffusive Waves, Cambridge University Press, Cambridge 1987. W. I. Fushchych, W. Shtelen, and N. Serov,Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics, Kluwer, Dordrecht 1993. P. J. Olver,Applications of Lie Groups to Differential Equations, Springer, New York 1986. W. I. Fushchych and P. I. Myronyuk, “Conditional symmetry and exact solutions of equations of nonlinear acoustics,”Dopov. Akad Nauk Ukr., No. 6, 23–39 (1991). N. I. Serov and B. W. Fushchych, “On a new nonlinear equation with unique symmetry,”Dopov. Akad. Nauk Ukr., No. 9, 49–50 (1994). P. N. Sionoid and A. T. Cates, “The generalized Bürgers and Zabolotskaya-Khokhlov equations: transformations, exact solutions and qualitative properties,”Proc. Royal Soc.,447, No. 1930, 253–270 (1994). W. I. Fushchych, “A new nonlinear equation for electromagnetic fields having velocity different from c,”Dopov. Akad. Nauk Ukr., No. 1, 24–27(1992). W. I. Fushchych, “Symmetry analysis,” in:Symmetry Analysis of Equations of Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 5–6. W. I. Fushchych and V. M. Boyko,Symmetry Classification of the One-Dimensional Second Order Equation of Hydrodynamical Type, Preprint LiTH-MATH-R-95-19, Linköping University, Sweden (1995). V. M. Boyko, “Symmetry classification of the one-dimensional second order equation of a hydrodynamical type,”J. Nonlin. Math. Phys.,2, No. 3–4, 418–424 (1995). V. I. Fushchych and V. M. Boiko, “Reduction of order and general solutions for some classes of equations of mathematical physics,”Dopov. Akad. Nauk Ukr., No. 9, 43–48 (1996).