Dromion-like structures in a (3+1)-dimensional KdV-type equation

Abstract

Dromion structures have been found in many (2 + 1)-dimensional models. The similar structure in (3 + 1) dimensions is studied in this paper for a KdV-type equation, . Starting from the bilinear form of the model, we found that there are five types of multi-dromion solutions for its potentials, say, . The first type of multi-dromion solution is driven by multi-camber solitons with one of them being non-parallel to the x-axis. The second, third and fourth types of multi-dromion solutions are driven by two camber solitons and one, two and three sets of parallel plane solitons, respectively. The fifth type of multi-dromion solution is driven by one set of parallel plane solitons, one set of camber solitons which are parallel to the x-axis and one camber soliton which is non-parallel to the x-axis. Phase shifts may be involved in the interactions among the multi-dromions for the first and fifth types of solutions. A single dromion solution of the model may possess quite a free shape. For instance, the point-like dromions, ring-type dromions, extended and sharp dromions and oscillatory dromions can be obtained by selecting some arbitrary functions appropriately.