On a class of nonlinear dispersive-dissipative interactions
Physica D - Special issue on nonlinear waves and solitons in physical systems
New solutions for a generalized Benjamin-Bona-Mahony-Burgers equation
MATH'08 Proceedings of the American Conference on Applied Mathematics
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One of the more interesting solutions of the integrable equation are the soliton solutions. In [20] Quiao and Liu proposed a new completely integrable equation which possesses peak solitons. In this work we study this equation from the point of view of the theory of symmetry reductions in partial differential equations. We obtain the classical symmetries admitted, then, we use the transformations groups to reduce the equations to ordinary differential equations. Physical interpretation of these reductions and some exact solutions are also provided. Among them we obtain a travelling wave with decaying velocity and an smooth soliton. solution.