SIMILARITY SOLUTIONS OF DISPERSIVE LONG-WAVE EQUATIONS IN 2 SPACE DIMENSIONS

In this paper, both the direct method and the non-classical Lie approa ch are applied to reduce the (2 + 1)-dimensional dispersive long wave equations. Nine types of two-dimensional PDE reductions and 13 types o f ODE reductions are given. All the known reductions obtained by the c lassical Lie approach are reobtained as some special cases. Similar to the (1 + 1)-dimensional case, some types of reductions with essential and logarithmic singular characteristic manifolds are allowed althoug h the model is integrable.