Exploring the interaction between lump, stripe and double-stripe, and periodic wave solutions of the Konopelchenko–Dubrovsky–Kaup–Kupershmidt system

Abstract The Konopelchenko–Dubrovsky–Kaup–Kupershmidt system has significant implications in various fields, including fluid mechanics, ocean dynamics, and plasma physics. This system includes various widely recognized nonlinear evolution equations as special cases. In this study, we present a systematic approach to identifying novel wave solutions to the system, examining various combinations of interactions between lumps, stripes, double stripes, and periodic waves. By strategically selecting the arbitrary free parameters, we incorporate various 2D and 3D profiles to clearly demonstrate the dynamic behaviors of the mixed localized wave structures. These graphical representations indicate that some of the identified solutions exhibit periodic wave propagation along a straight line at specific angles to the spatial axes, maintaining constant wavelengths, amplitudes, and velocities. The solutions proposed in this study provide valuable insights into the mechanisms of wave propagation across diverse physical domains. Furthermore, the approach outlined herein is versatile and can be applied to various nonlinear differential equations in mathematical physics.