N-Soliton Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg--de Vries Equation
XU Xiao-Ge1,2,4, MENG Xiang-Hua3, GAO Yi-Tian2
1School of Science, Beijing University of Aeronautics and Astronautics, Beijing 1000832Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 1000833School of Science, Beijing University of Posts and Telecommunications, Beijing 1008764Beijing Information Technology Institute, Beijing 100101
N-Soliton Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg--de Vries Equation
XU Xiao-Ge1,2,4, MENG Xiang-Hua3, GAO Yi-Tian2
1School of Science, Beijing University of Aeronautics and Astronautics, Beijing 1000832Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 1000833School of Science, Beijing University of Posts and Telecommunications, Beijing 1008764Beijing Information Technology Institute, Beijing 100101
We concentrate on finding exact solutions for a generalized variable-coefficient Korteweg--de Vries equation of physically significance. The analytic N-soliton solution in Wronskian form for such a model is postulated and verified by direct substituting the solution into the bilinear form by virtue of the Wronskian technique. Additionally, the bilinear auto-Bäcklund transformation between the (N-1)- and N-soliton solutions is verified.
We concentrate on finding exact solutions for a generalized variable-coefficient Korteweg--de Vries equation of physically significance. The analytic N-soliton solution in Wronskian form for such a model is postulated and verified by direct substituting the solution into the bilinear form by virtue of the Wronskian technique. Additionally, the bilinear auto-Bäcklund transformation between the (N-1)- and N-soliton solutions is verified.
[1] Lamb G L Jr 1980 Elements of Soliton Theory (New York: Wiley) [2] Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge: Cambridge University Press) Bullough R K and Caudrey P J 1980 Solitons (Berlin: Springer) [3] Gardner C S, Greene J M, Kruskal M D and Miura R M 1967 Phys. Rev. Lett. 19 1095 Gardner C S, Greene J M, Kruskal M D and Miura R M 1974 Commun. Pure Appl. Math. 27 97 [4] Ablowitz M J, Kaup D J, Newell A C and Segur H 1973 Phys. Rev. Lett. 30 1262 Ablowitz M J, Kaup D J, Newell A C and Segur H 1973 Phys. Rev. Lett. 31 125 [5] Hirota R 1971 Phys. Rev. Lett. 27 1192 Hirota R 1974 Prog. Theor. Phys. Suppl. 52 1498 Hirota R, Hu X and Tang X 2003 J. Math. Anal. Appl. 288 326 Hu X B 1994 J. Phys. A: Math. Gen. 27 1331 [6] Satsuma J 1979 J. Phys. Soc. Jpn. 46 395 [7] Freeman N C and Nimmo J J C 1983 Phys. Lett. A 95 1 Nimmo J J C and Freeman N C 1983 Phys. Lett. A 95 4 [8] Chan W L and Zhang X 1994 J. Phys. A 27 407 [9] Zhao X Q, Tang D B and Wang L M 2005 Phys. Lett. A 346 288 [10] Ding S S, Sun W J and Zhu D C 2008 Appl. Math. Comput. 199 268 [11] Zhang D J and Chen D Y 2004 J. Phys. A 37 851 [12] Xu X G, Meng X H and Gao Y T 2008 Nonlinear Anal. (submitted) [13] Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
2008, Vol. 25 
