On the two-dimensional regularized long-wave equation in fluids and plasmas

Summary.  To the two-dimensional regularized long-wave equation we perform computerized symbolic computation to obtain a new auto-B?cklund transformation and picture out some new bell-shaped and anti-bell-shaped solitary waves, which could help in the investigations on the Rossby waves in rotating fluids and the drift waves in plasmas. Received January 8, 2002; revised April 18, 2002 Published online: February 10, 2003 Acknowledgements We thank the editor Prof. N. Aksel and the referees for their valuable comments. This work has been supported by the Excellent Young Teachers Program of the Ministry of Education of China, by the National Key Basic Research Special Foundation (NKBRSF) of China under Grant No.␣G1999032701, by the China Talent Fund, by the National Natural Science Foundation of China under Grant No. 10272017, by the W. T. Wu Foundation on Mathematics Mechanization, by the Talent Construction Special Fund and Basic-Sciences Doctoral Education Fund of Beijing University of Aeronautics and Astronautics. BT also thanks the Enterprise Chair Professors Programme of the Bright Oceans Inter-Telecom Corporation and Beijing University of Posts and Telecommunications. YTG would like to acknowledge the Cheung Kong Scholars Programme of the Ministry of Education of China and Li Ka Shing Foundation of Hong Kong.