Revisitation of the localized excitations of the \((2+1)\)-dimensional KdV equation (Q2716204)

Starting from a Bäcklund transformation and using the variable separation approach for the \((2+1)\)-dimensional ANNV equation, the authors obtain many new types of multi-soliton solutions because of the existence of the arbitrary functions appearing in the seed solution and in the variable separation procedure. By selecting the arbitrary functions appropriately, the multiple localized solutions may be dromions, lumps, ring solitons, breathers, instantons, etc.