Traveling-wave solutions of the Calogero-Degasperis-Fokas equation in 2+1 dimensions

Soliton solutions are among the more interesting solutions of the (2+1)-dimensional integrable Calogero-Degasperis Fokas (CDF) equation. We previously derived a complete group classification for the CDF equation in 2+1 dimensions. Using classical Lie symmetries, we now consider traveling-wave reductions with a variable velocity depending on an arbitrary function. The corresponding solutions of the (2+1)dimensional equation involve up to three arbitrary smooth functions. The solutions consequently exhibit a rich variety of qualitative behaviors. Choosing the arbitrary functions appropriately, we exhibit solitary waves and bound states.