TY - JOUR
T1 - Bäcklund transformation and analytic solutions for a generalized variable-coefficient modified korteweg-de vries model from fluid dynamics and plasmas
AU - Sun, Fu Wei
AU - Gao, Yi Tian
AU - Zhang, Chun Yi
AU - Xu, Xiao Ge
PY - 2008/11
Y1 - 2008/11
N2 - We investigate a generalized variable-coefficient modified Korteweg-de Vries model with perturbed factor and external force (vc-GmKdV) describing fluid dynamics and space plasmas. In this paper, we propose an extended variable-coefficient balancing-act method (Evc-BAM), which is concise and straightforward, to obtain the generalized analytic solutions including solitary wave solution of the vc-GmKdV model with symbolic computation. Meanwhile, using the Evc-BAM, we obtain an auto-Bäcklund transformation for the vc-GmKdV model on the relevant constraint conditions of the coefficient functions. Using the given auto-Bäcklund transformation, the solutions of special equations for the vc-GmKdV model are also obtained as the variable-coefficient Korteweg-de Vries (vc-KdV) equation, the generalized KdV equation with perturbed factor and external force (GKdV), the variable-coefficient modified Korteweg-de Vries (vc-mKdV) equation, and the variable-coefficient cylindrical modified Korteweg-de Vries (vc-cmKdV) equation, respectively.
AB - We investigate a generalized variable-coefficient modified Korteweg-de Vries model with perturbed factor and external force (vc-GmKdV) describing fluid dynamics and space plasmas. In this paper, we propose an extended variable-coefficient balancing-act method (Evc-BAM), which is concise and straightforward, to obtain the generalized analytic solutions including solitary wave solution of the vc-GmKdV model with symbolic computation. Meanwhile, using the Evc-BAM, we obtain an auto-Bäcklund transformation for the vc-GmKdV model on the relevant constraint conditions of the coefficient functions. Using the given auto-Bäcklund transformation, the solutions of special equations for the vc-GmKdV model are also obtained as the variable-coefficient Korteweg-de Vries (vc-KdV) equation, the generalized KdV equation with perturbed factor and external force (GKdV), the variable-coefficient modified Korteweg-de Vries (vc-mKdV) equation, and the variable-coefficient cylindrical modified Korteweg-de Vries (vc-cmKdV) equation, respectively.
KW - Analytic solutions
KW - Auto-Bäcklund transformation
KW - Extended variable-coefficient balancing-act method
KW - Fluids
KW - Plasmas
KW - Variable-cofficient modified KdV model
UR - https://www.scopus.com/pages/publications/57349124498
U2 - 10.1142/S0129183108013199
DO - 10.1142/S0129183108013199
M3 - 文章
AN - SCOPUS:57349124498
SN - 0129-1831
VL - 19
SP - 1659
EP - 1671
JO - International Journal of Modern Physics C
JF - International Journal of Modern Physics C
IS - 11
ER -