Hybrid localized wave solutions for a generalized Calogero-Bogoyavlenskii-Konopelchenko-Schiff system in a fluid or plasma

Based on the long wave limit method and complex conjugate condition technique, we investigate hybrid localized wave solutions with different forms for the generalized Calogero-Bogoyavlenskii-Konopelchenko-Schiff system. Four kinds of bilinear auto-Backlund transformations are constructed by constructing different equivalent exchange formulas. The system simulates the formation of localized waves on the ocean surface and the interaction among water waves. In order to better analyze the dynamic characteristics of hybrid localized wave solutions, several three-dimensional diagrams are drawn with the help of Mathematica software. Besides, seven kinds of combined waves are summarized, including the hybrid solutions consisting of L-order kink waves, Q-order breather waves and M-order lump waves. Water wave phenomena can be simulated by nonlinear evolution equations. Analyzing the images of analytic solutions is helpful to understand the dynamic behavior of these models. We hope that bilinear auto-Backlund transformations and hybrid localized wave solutions can help researchers simulate nonlinear phenomena in the fields of hydrodynamics,oceanography,ionospheric physics, optics, condensed state physics and so on.

Automated summary

This paper investigates hybrid localized wave solutions with different forms for the generalized Calogero-Bogoyavlenskii-Konopelchenko-Schiff system using the long wave limit method and complex conjugate condition technique. Four kinds of bilinear auto-Backlund transformations are constructed by constructing different equivalent exchange formulas. Three-dimensional diagrams are drawn to better analyze the dynamic characteristics of the solutions. Seven kinds of combined waves are summarized, including the hybrid solutions consisting of L-order kink waves, Q-order breather waves, and M-order lump waves.