Hybrid soliton, breather waves and solution molecules of the (2+1)-dimensional generalized fifth-order KdV equation

Abstract

In this paper, we take the (2+1)-dimensional generalized fifth-order KdV (fKdV) equation as an example. We obtain many wave solutions, including hybrid soliton, breather waves and solution molecules. In order to solve hybrid soliton, we give two transformation forms. For Transform one, real and complex parameters lead to different wave solutions. Soliton solutions are obtained when the parameter values are real, but some breather waves appear when the parameter values are complex. When the parameter value changes, the number of solitons and the position of the waves will also change. For Transform two, we assign the parameter values to real values and obtain the corresponding two-, three- and four-soliton solutions. The most important thing is that, on the basis of Transform one, we add different constraint conditions according to different coordinate systems, and finally get a very interesting phenomenon: soliton molecules. In addition, we give not only the three-dimensional plots but also the density plots. In general, these results will enrich the existing literature on the (2+1)-dimensional generalized fKdV equation and help to understand this kind of KdV equation.