Bäcklund transformation for analyzing a cylindrical Korteweg–de Vries equation and investigating multiple soliton solutions in a plasma

Abstract

The presence of the geometrical curvature makes the planar Korteweg–de Vries (KdV) equation inadequate to describe the propagation of nonlinear waves. In many scientific disciplines including plasma physics, nonlinear optics, oceanography, and communications, the cylindrical KdV (CKdV) equation becomes the appropriate choice for modeling these waves. Motivated by these applications, the Bäcklund transformation is used to analyze and find an analytical solution to the CKdV equation in the present investigation. For the first time, the multi-soliton solutions, including single-, two-, and three-soliton solutions, are investigated, and a general scheme is given to find N-soliton solutions of the CKdV equation in the context of plasma physics. Numerous researchers may find the given solutions helpful in understanding the mechanism of the generation of multi-solitons in their laboratory experiments and may also engender interest in the space physics community to look for these structures in the data coming from a variety of satellites roaming in space.