Bell-Polynomial Approach and Soliton Solutions for Some Higher-Order Korteweg-de Vries Equations in Fluid Mechanics, Plasma Physics and Lattice Dynamics

摘要

The Korteweg-de Vries (KdV)-type equations have been seen in fluid mechanics, plasma physics and lattice dynamics, etc. This paper will address the bilinearization problem for some higher-order KdV equations. Based on the relationship between the bilinear method and Bell-polynomial scheme, with introducing an auxiliary independent variable, we will present the general bilinear forms. By virtue of the symbolic computation, one- and two-soliton solutions are derived.