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 classiffication 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.