Abstract
This paper is concerned with the general regular long-wave (RLW) types of equations. By the combination of Painleve analysis and Lie group classification method, the conditional Painleve property (PP) and Backlund transformations (BTs) of the nonlinear wave equations are provided under some conditions. Then, all of the point symmetries of the nonlinear RLW types of equations are obtained, the exact solutions to the equations are investigated. Particularly, some explicit solutions are provided by the special function and Φ-expansion method.
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