LIE SYMMETRY AND EXACT SOLUTION OF (2+1)-DIMENSIONAL GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION WITH VARIABLE COEFFICIENTS

Abstract

The simple direct method is adopted to find Non-Auto-Backlund transformation for variable coefficient non-linear systems. The (2+1)-dimensional generalized Kadomtsev-Petviashvili equation with variable coefficients is used as an example to elucidate the solution procedure, and its symmetry transformation and exact solutions are obtained.

Dates

  • Submission Date2013-03-02
  • Revision Date2013-04-24
  • Acceptance Date2013-04-30
  • Online Date2013-12-28

DOI Reference

10.2298/TSCI1305490M

References

  1. Filippov, A. T., The Versatile Soliton, Springer, London, 2010
  2. Olver, P. J., Applications of Lie Groups to Differential Equations, Springer, New York, USA, 2000
  3. Lou, S. Y., et al., Virasoro Structure and Localized Excitations of the LKR System, Journal of Mathematical Physics, 44 (2003), 12, pp. 5869-5887
  4. Lou, S., Ma, H.-C., Non-Lie Symmetry Groups of (2+1)-Dimensional Non-linear Systems Obtained from a Simple Direct Method, Journal of Physics A: Mathematical and General, 38 (2005), 7, pp. L129-L137
  5. Clarkson, P. A., Kruskal, M. D., New Similarity Reductions of the Boussinesq Equation, Journal of Mathematical Physics, 30 (1989), 10, pp. 2201-2213
  6. Ablowitz, M. J., Segur, H., On the Evolution of Packets of Water Waves, Journal of Fluid Mechanics, 92 (1979), 4, pp. 691-715
  7. Kadomtsev, B. B., Petviashvili, V. I., On the Stability of Solitary Waves in Weakly Dispersive Media, Soviet Physics Doklady, 15 (1970), 6, pp. 539-541
  8. Tian, B., Gao, Y.-T., Truncated Painleve Expansion and a Wide-Ranging Type of Generalized Variable- Coefficient Kadomtsev-Petviashvili Equations, Physics Letters A, 209 (1995), 5-6, pp. 297-304
  9. Tian, B., Gao, Y.-T., Spherical Kadomtsev-Petviashvili Equation and Nebulons for Dust Ion-Acoustic Waves with Symbolic Computation, Physics Letters A, 340 (2005), 1-4, pp. 243-250
  10. Gao, Y.-T., Tian, B., Cylindrical Kadomtsev-Petviashvili Model, Nebulons and Symbolic Computation for Cosmic Dust Ion-Acoustic Waves, Physics Letters A, 349 (2006), 5, pp. 314-319
  11. Yan, Z., Backlund Transformation, Non-Local Symmetry and Exact Solutions for (2+1)-Dimensional Variable Coefficient Generalized KP Equations, Communications in Non-linear Science and Numerical Simulation, 5 (2000), 1, pp. 31-35
  12. Yomba, E., Construction of New Soliton-Like Solutions for the (2+1) Dimensional KdV Equation with Variable Coefficients, Chaos, Solitons & Fractals, 21 (2004), 1, pp. 75-79
  13. Elwakil, S. A., et al., New Exact Solutions for a Generalized Variable Coefficients 2D KdV Equation, Chaos, Solitons & Fractals, 19 (2004), 5, pp. 1083-1086
  14. Xuan, H.-N., et al., Families of Non-Travelling Wave Solutions to a Generalized Variable Coefficient Two-Dimensional KdV Equation Using Symbolic Computation, Chaos, Solitons & Fractals, 23 (2005), 1, pp. 171-174
  15. Sun, Y.-P., Tam, H., Grammian Solutions and Pfaffianization of a Non-Isospectral and Variable- Coefficient Kadomtsev-Petviashvili Equation, Journal of Mathematical Analysis and Applications, 343 (2008), 2, pp. 810-817
  16. Yao, Z.-Z. et al., Wronskian and Grammian Determinant Solutions for a Variable-Coefficient Kadomtsev- Petviashvili Equation, Communications in Theoretical Physics, 49 (2008), 5, pp. 1125-1128
  17. Ye, L., et al., Grammian Solutions to a Variable-Coefficient KP Equation, Chinese Physics Letters, 25 (2008), 2, pp. 357-358
  18. Lu, Z., Xie, F., Explicit Bi-Soliton-Like Solutions for a Generalized KP Equation with Variable Coefficients, Mathematical and Computer Modelling, 52 (2010), 9-10, pp. 1423-1427
Volume 17, Issue 5, Pages1490 -1493