Painlevé analysis, Lie symmetries and exact solutions for (2+1)-dimensional variable coefficients Broer-Kaup equations

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 4, 2012, Pages 1529-1541

  Kumar, Sachin ^a   Singh, K ^b   Gupta, R K ^a  

^a THAPAR UNIVERSITY   (India)

^b JAYPEE UNIVERSITY OF INFORMATION TECHNOLOGY   (India)

Author keywords

Exact solutions; Lie classical method; Painlev analysis

Indexed keywords

LIE GROUPS; ORDINARY DIFFERENTIAL EQUATIONS;

BROER KAUP EQUATION; BROER-KAUP SYSTEM; EXACT SOLUTION; KP EQUATION; LIE CLASSICAL METHODS; LIE SYMMETRIES; MATHEMATICAL PHYSICS; PAINLEVÉ ANALYSE; SYMMETRIES AND EXACT SOLUTIONS; VARIABLE COEFFICIENTS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 80055021223     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.09.003     Document Type: Article

References (26)

1. Lou S.Y., Hu X.B. Infinitely many Lax pairs and symmetry constraints of the KP equation. J Math Phys 1997, 38:6401-6427.
2. Yan Z.Y., Zhang H.Q. Symbolic computation and new families of exact soliton-like solutions to the integrable Broer-Kaup (BK) equations in (2+1)-dimensional spaces. J Phys A Math Gen 2001, 34:1785-1792.
3. Lou S.Y., Hu X.B. Broer-Kaup systems from Darboux transformation related symmetry constraints of Kadomtsev-Petviashvili equation. Commun Theor Phys (Beijing, China) 1998, 29:145-148.
4. Wang M.L., Wang Y.M. A new Bäcklund transformation and multi-soliton solutions to the KdV equation with general variable coefficients. Phys Lett A 2001, 287(3-4):211-216.
5. Engui F. Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations. Phys Lett A 2002, 294(1):26-30.
6. Singh K., Gupta R.K. Lie symmetries and exact solutions of a new generalized Hirota-Satsuma coupled KdV system with variable coefficients. Int J Eng Sci 2006, 44:241-255.
7. Singh K., Gupta R.K., Kumar S. Benjamin-Bona-Mahony (BBM) equation with variable coefficients: similarity reductions and Painlevé analysis. Appl Math Comput 2011, 217:7021-7027.
8. Hanze L., Jibin L., Lei L. Painlev analysis, Lie symmetries, and exact solutions for the time-dependent coefficients Gardner equations. Nonlinear Dyn 2010, 59:497-502.
9. Olver P.J. Applications of Lie groups to differential equations 1993, Springer-Verlag.
10. Bluman G.W., Kumei S. Symmetries and differential equations. Applied mathematical science 1989, Springer, Berlin.
11. Zhang J.F., Han P. Localized coherent structures of the (2+1)-dimensional higher order Broer-Kaup equations. Acta Phys Sin 2002, 51:705-711.
12. Ma S.H., Ren Q.B., Fang J.P., Zheng C.L. Special soliton structures and the phenomena of fission and annihilation of solitons for the(2+1)-dimensional Broer-Kaup system with variable coefficients. Acta Phys Sin 2007, 56:6777-6807.
13. Bangqing L., Yulan M. The non-traveling wave solutions and novel fractal soliton for the (2+1)-dimensional Broer-Kaup equations with variable coefficients. Commun Nonlinear Sci Numer Simul 2011, 16:144-149.
14. Huang W.H. Periodic semifolded solitary waves for (2+1)-dimensional variable coefficient Broer-Kaup system. Commun Theor Phys 2008, 49:1383-1388.
15. Weiss J., Tabor M., Carnevale G. The Painlevé property for partial differential equations. J Math Phys 1983, 24:522-526.
16. Jimbo M., Kruskal M.D., Miwa T. Painlevé test for the self-dual Yang-Mills equation. Phys Lett A 1982, 92:59-60.
17. Singh K., Gupta R.K. Symmetry analysis and some exact solutions of cylindrically symmetric null fields in general relativity. Commun. Nonlinear Sci. Numer. Simul 2011, 16:4189-4196.
18. Popovych R.O., Sophocleous, Vaneeva O.O. Exact solutions of a remarkable fin equation. Appl Math Lett 2008, 21:209-214.
19. Bluman G., Broadbridge P., King J.R., Ward M.J. Similarity:generalizations, applications and open problems. J Eng Math 2010, 66:1-9.
20. Tychynin V., Rasin O. Nonlocal symmetry and generating solutions for the inhomogeneous Burgers equation. Proc Inst Math NAS Ukraine 2004, 50:277-281.
21. Schulze-Halberg A., Jiménez J.M.C. Darboux transformations for the time-dependent nonhomogeneous Burgers equation in (1+1) dimensions. Phys Scr 2009, 80:065014. 8pp.
22. Burgers J.M. The nonlinear diffusion equation: asymptotic solutions and statistical problems 1974, Reidel-Dordrecht.
23. xx. Commun Pure Appl Math 1950, 3:201-230.
24. Gandarias M.L., Bruzon M.S. Nonclassical potential symmetries for the Burgers equation. Nonlinear Anal 2009, 71:1826-1834.
25. Ivanova N.M., Sophocleous C., Tracinà R. Lie group analysis of two-dimensional variable-coefficient Burgers equation. Z Angew Math Phys 2010, 61:793-809.
26. Nadjafikhah M., Bakhshandeh-Chamazkoti R. Symmetry group classification for general Burger's equation. Commun Nonlinear Sci Numer Simul 2010, 15:2303-2310.