Eur. Phys. J. B 22, 351-360 (2001)
https://doi.org/10.1007/s100520100796

Variable-coefficient balancing-act method and variable-coefficient KdV equation from fluid dynamics and plasma physics

¹ Department of Applied Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
² CCAST (World Lab.), PO Box 8730, Beijing 100080, China and Department of Applied Physics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China (Mailing address)

Corresponding author: ^a gaoyt@public.bta.net.cn

Received: 23 December 2000
Revised: 12 March 2001
Published online: 15 August 2001

Abstract

Although their coefficient functions often make the studies very hard, the variable-coefficient nonlinear evolution equations (vcNLEEs) are of current interests since they are able to model the real world in many fields of physical and engineering sciences. In this paper, based on the computerized symbolic computation, a variable-coefficient balancing-act method is proposed. Being concise and straightforward, it can be applicable to certain vcNLEEs, to get the solitonic features out, along with other exact analytic solutions, all beyond the travelling waves. By virtue of the method, such new solutions are demonstrated for a variable-coefficient KdV equation arising from fluid dynamics, plasmas and other fields. Special attention is paid to the one- and two-soliton-type solutions. Sample applications and physical interests are discussed, such as coastal waters of the world oceans, plasma physics, liquid drops and bubbles. Nonlinear interaction hallmarked by the phase shifts is pictured. Comparisons are made with other results in the literature.