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

Abstract

In a previous paper (Lou S-y 1995 J. Phys. A: Math. Gen. 28 7227), a generalized dromion structure was revealed for the (2+1)-dimensional KdV equation, which was first derived by Boiti et al (Boiti M, Leon J J P, Manna M and Pempinelli F 1986 Inverse Problems 2 271) using the idea of the weak Lax pair. In this paper, using a Bäcklund transformation and the variable separation approach, we find there exist much more abundant localized structures for the (2+1)-dimensional KdV equation. The abundance of the localized structures of the model is introduced by the entrance of an arbitrary function of the seed solution. Some special types of dromion solution, lumps, breathers, instantons and the ring type of soliton, are discussed by selecting the arbitrary functions appropriately. The dromion solutions can be driven by sets of straight-line and curved-line ghost solitons. The dromion solutions may be located not only at the cross points of the lines but also at the closed points of the curves. The breathers may breathe both in amplitude and in shape.