Interactions among periodic waves and solitary waves for a higher dimensional system

Abstract

The general variable separated approach is successfully extended to the (2+1)-dimensional physical model and we obtain a universal formula involving arbitrary number of variable separated functions. Because of the existence of the arbitrary functions in the universal formula, many new types of structures of periodic waves, for example, the periodic–periodic interaction waves, periodic–kink interaction waves, periodic–peakon interaction waves, periodic–compacton interaction waves, periodic–foldon interaction waves, etc, are investigated both analytically and graphically. Some novel features or interesting behaviours are revealed.