Bilinear form, solitons, breathers, lumps and hybrid solutions for a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation

In this work, we study a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation for the nonlinear dispersive waves in an inhomogeneous medium. Bilinear form and N-soliton solutions are derived, where N is a positive integer. The higher-order breather and lump solutions are constructed based on the N-soliton solutions. Hybrid solutions comprising the solitons and breathers, breathers and lumps, as well as solitons and lumps are worked out. Amplitudes and velocities of the one solitons as well as periods of the first-order breathers are investigated. Amplitudes of the first-order lumps reach the maximum and minimum values at certain points given in the paper. Interactions between any two of those waves are discussed graphically.

Automated summary

This work focuses on a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation for nonlinear dispersive waves in an inhomogeneous medium. It derives bilinear form and N-soliton solutions, constructs higher-order breather and lump solutions based on these solitons, and investigates the interactions between different types of waves.