OJAppS  Vol.3 No.1 B1 , April 2013
Nonsingular Positon Solutions of a Variable-Coefficient Modified KdV Equation
ABSTRACT

The determinant representation of three-fold Darboux transformation for a variable-coefficient modified KdV equation is displayed based on the technique used to solve Ablowitz-Kaup-Newell-Segur system. Additionally, the nonsingular positon solutions of the variable-coefficient modified KdV equation are firstly discovered analytically and graphically.


Cite this paper
Y. Lin, C. Li and J. He, "Nonsingular Positon Solutions of a Variable-Coefficient Modified KdV Equation," Open Journal of Applied Sciences, Vol. 3 No. 1, 2013, pp. 102-105. doi: 10.4236/ojapps.2013.31B1021.
References
[1]   V. N. Serkin and A. Hasegawa, “Novel Soliton Solutions of the Nonlinear Schrödinger Equation Model,” Physical Review Letters, Vol. 85, No. 21, 2000, pp. 4502-4505. doi:10.1103/PhysRevLett.85.4502

[2]   Y. Zhang, J. B. Li and Y. N. Lv, “The Exact Solution and Integrable Properties to the Variable-Coefficient Modified Korteweg-de Vries Equation,” Annals of Physics, Vol. 323, No. 12, 2008, pp. 3059-3064. doi:10.1016/j.aop.2008.04.012

[3]   L. Wang, Y. T. Gao and F. H. Qi, “N-fold Darboux Transformation and Double-Wronskian-typed Solitonic Structures for a Variable-Coefficient Modified Kortweg-de Vries Equation,” Annals of Physics,Vol. 327, No. 8, 2012, pp. 1974-1988. doi:10.1016/j.aop.2012.04.009

[4]   V. B. Matveev, “Positon-Politon and Soliton-Positon Collisions: KdV case,” Physical Letters A, Vol. 166, No. 3-4,1992, pp. 209-212. doi:10.1016/0375-9601(92)90363-Q

[5]   V. B. Matveev and Positons, “Slowly Decreasing Analogues of Solitons,” Theoretical and Mathematical Physics, Vol. 131 No. 1, 2002, pp. 483-497. doi:10.1023/A:1015149618529

[6]   H. C. Hu, B. Tong and S. Y. Lou, “Nonsingular Positon and Complexi-Ton Solutions for the Coupled KdV System,” Physics Letters A, Vol. 351, No. 6, 2006, pp. 403-412. doi:10.1016/j.physleta.2005.11.047

[7]   J. S. He, H. R. Zhang, L. H. Wang, K. Porsezian and A. S. Fokas, “A Generating Mechanism for Higher Order Rogue Waves,” 2013.

[8]   J. S. He, L. Zhang, Y. Cheng and Y. S. Li, “Determinant Representation of Darboux Transformation for the AKNS System,” Science in China Series A: Ma-thematics, Vol. 49, No. 12, 2006, pp. 1867-1878. doi:10.1007/s11425-006-2025-1

[9]   K. Porsezian and K. Nakkeeran, “Optical Solitons in Presence of Kerr Dispersion and Self-Frequency Shift,” Physical Review Letters, Vol. 76, No. 21, 1996, pp. 3955-3958. doi:10.1103/PhysRevLett.76.3955

[10]   M. J. Ablowitz, D. J. Kaup, A .C. Newell, H. Seger, “Nonlinear-Evolution Equations of Physical Significance,” Physical Review Letters, Vol. 31, No. 2, 1973, pp. 125-127. doi:10.1103/PhysRevLett.31.125

[11]   H. H. Chen and C. S. Liu, “Soliton in Nonuniform Media,” Physical Review Letters, Vol. 37, No.11, 1976, pp. 693-697. doi:10.1103/PhysRevLett.37.693

 
 
Top