Resumen de Bilinear Forms, Bilinear Auto-Bäcklund Transformations and Similarity Reductions for a (3+1)-Dimensional Generalized Variable-Coefficient Korteweg-de VriesCalogero-Bogoyavlenskii-Schiff Equation in Quantum and Fluid Mechanics
Xin Yi Gao, Wei Gang Zhao, Da Wei Zuo
In quantum and fluid mechanics, nonlinear models are reported, including a (3+1)- dimensional generalized variable-coefficient Korteweg-de Vries-Calogero-Bogoy avlenskii-Schiff equation describing the interaction between a long wave and a Riemann wave, which is the subject of this paper. For that equation, we find (A) a bilinear form, (B) a set of the bilinear auto-Bäcklund transformations with some soliton solutions and (C) a set of the similarity reductions. Our results, i.e., bilinear form, bilinear auto-Bäcklund transformations with solitons as well as similarity reductions, may help people investigate certain wave modes and dynamic features in quantum and fluid mechanics in the future.
