Perturbation, symmetry analysis, Bäcklund and reciprocal transformation for the extended Boussinesq equation in fluid mechanics

Abstract

Abstract In this work, we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics, scientific fields, and ocean engineering. This equation will be reduced to the Korteweg–de Vries equation via using the perturbation analysis. We derive the corresponding vectors, symmetry reduction and explicit solutions for this equation. We readily obtain Bäcklund transformation associated with truncated Painlevé expansion. We also examine the related conservation laws of this equation via using the multiplier method. Moreover, we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.