Soliton solutions and integrability for the generalized variable-coefficient extended Korteweg–de Vries equation in fluids

In this work, we investigate the generalized variable-coefficient extended Korteweg–de Vries equation in fluid dynamics. Through the binary Bell polynomials, more general bilinear form and N -soliton solutions than the existing ones are presented. Besides, two types of the Bäcklund transformation are derived. Based on the Bäcklund transformation in the binary-Bell-polynomial form, Lax pair is constructed as well.