TY - JOUR
T1 - Darboux transformation and explicit solutions for the integrable sixth-order KdV equation for nonlinear waves
AU - Wen, Xiao Yong
AU - Gao, Yi Tian
AU - Wang, Lei
PY - 2011/9/1
Y1 - 2011/9/1
N2 - Korteweg-de Vries (KdV)-type equations can describe some physical phenomena in fluids, nonlinear optics, quantum mechanics, plasmas, etc. In this paper, with the aid of symbolic computation, the integrable sixth-order KdV equation is investigated. Darboux transformation (DT) with an arbitrary parameter is presented. Explicit solutions are derived with the DT. Relevant properties are graphically illustrated, which might be helpful to understand some physical processes in fluids, plasmas, optics and quantum mechanics.
AB - Korteweg-de Vries (KdV)-type equations can describe some physical phenomena in fluids, nonlinear optics, quantum mechanics, plasmas, etc. In this paper, with the aid of symbolic computation, the integrable sixth-order KdV equation is investigated. Darboux transformation (DT) with an arbitrary parameter is presented. Explicit solutions are derived with the DT. Relevant properties are graphically illustrated, which might be helpful to understand some physical processes in fluids, plasmas, optics and quantum mechanics.
KW - Darboux transformation
KW - Explicit solution
KW - Integrable sixth-order KdV equation
KW - Lax pair
KW - Symbolic computation
UR - https://www.scopus.com/pages/publications/79959749287
U2 - 10.1016/j.amc.2011.05.045
DO - 10.1016/j.amc.2011.05.045
M3 - 文章
AN - SCOPUS:79959749287
SN - 0096-3003
VL - 218
SP - 55
EP - 60
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 1
ER -