Some traveling wave solutions for the dissipative Zabolotskaya-Khokhlov equation

By using the theory of nonclassical symmetry reductions, some traveling wave solutions of the dissipative Zabolotskaya Khokhlov equation are obtained. In particular, we derive some singular rational traveling wave solutions describing coherent structures traveling with constant velocity.

[1]  M. Bruzón,et al.  Classical and nonclassical symmetries for a Kuramoto–Sivashinsky equation with dispersive effects , 2007 .

[2]  A. Rozanova,et al.  The Khokhlov-Zabolotskaya-Kuznetsov equation , 2007 .

[3]  Maria Luz Gandarias,et al.  Applying a new algorithm to derive nonclassical symmetries , 2006 .

[4]  A. Rozanova.  Equation de Khokhlov-Zabolotskaya-Kuznetsov : analyse mathématique, validation de l'approximation et méthode de contrôle , 2006 .

[5]  Nicoleta Bila,et al.  On a new procedure for finding nonclassical symmetries , 2004, J. Symb. Comput..

[6]  Peter A. Clarkson,et al.  Nonclassical symmetry reductions of the Boussinesq equation , 1995 .

[7]  M. Tajiri.  Similarity Reductions of the Zabolotskaya-Khokhlov Equation with a Dissipative Term , 1995 .

[8]  Elizabeth L. Mansfield,et al.  Algorithms for the Nonclassical Method of Symmetry Reductions , 1994, SIAM J. Appl. Math..

[9]  N. I. Serov,et al.  Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics , 1993 .

[10]  P. Clarkson,et al.  Nonclassical symmetry reductions and exact solutions of the Zabolotskaya–Khokhlov equation , 1992, European Journal of Applied Mathematics.

[11]  T. Taniuti.  Reductive perturbation method for quasi one-dimensional nonlinear wave propagation. I , 1990 .

[12]  A. Chowdhury,et al.  Towards the conservation laws and Lie symmetries for the Khokhlov-Zabolotskaya equation in three dimensions , 1986 .

[13]  E. Zabolotskaya,et al.  Quasi-plane waves in the nonlinear acoustics of confined beams , 1969 .