Symbolic Computation Study Of A Generalized Variable Coefficient ...
Symbolic Computation Study of a Generalized Variable-Coefficient
Two-Dimensional Korteweg-de Vries Model with Various External-Force
Terms from Shallow Water Waves, Plasma Physics, and Fluid Dynamics
Xing L¨ua, Li-Li Lia, Zhen-Zhi Yaoa, Tao Genga, Ke-Jie Caia, Cheng Zhanga,
and Bo Tiana,b,c
a School of Science, P. O. Box 49, Beijing University of Posts and Telecommunications,
Beijing 100876, China
b State Key Laboratory of Software Development Environment, Beijing University of Aeronautics
and Astronautics, Beijing 100191, China
c Key Laboratory of Optical Communication and Lightwave Technologies, Ministry of Education,
Beijing University of Posts and Telecommunications, Beijing 100876, China
Reprint requests to X. L.; E-mail: xinglv655@yahoo.com.cn
Z. Naturforsch. 64a, 222 – 228 (2009); received April 8, 2008 / revised August 4, 2008
The variable-coefficient two-dimensional Korteweg-de Vries (KdV) model is of considerable sig-
nificance in describing many physical situations such as in canonical and cylindrical cases, and in the
propagation of surface waves in large channels of varying width and depth with nonvanishing vor-
ticity. Under investigation hereby is a generalized variable-coefficient two-dimensional KdV model
with various external-force terms. With the extended bilinear method, this model is transformed into
a variable-coefficient bilinear form, and then a B¨acklund transformation is constructed in bilinear
form. Via symbolic computation, the associated inverse scattering scheme is simultaneously derived
on the basis of the aforementioned bilinear B¨acklund transformation. Certain constraints on coef-
ficient functions are also analyzed and finally some possible cases of the external-force terms are
discussed.
Key words: Generalized Variable-Coefficient Two-Dimensional Korteweg-de Vries Model;
Symbolic Computation; B¨acklund Transformation; Variable-Coefficient Bilinear Form;
Inverse Scattering Scheme.
