Exact solutions of the Swift-Hohenberg equation with dispersion

Communications in Nonlinear Science and Numerical Simulation

Volumn 17, Issue 1, 2012, Pages 26-34

  Kudryashov, Nikolai A ^a   Sinelshchikov, Dmitry I ^a  

^a NATIONAL RESEARCH NUCLEAR UNIVERSITY MEPHI   (Russian Federation)

Author keywords

Dispersion; Meromorphic exact solutions; Swift Hohenberg equation

Indexed keywords

EXACT SOLUTION; MEROMORPHIC EXACT SOLUTION; MEROMORPHIC SOLUTIONS; SWIFT-HOHENBERG EQUATIONS; TRAVELING WAVE SOLUTION;

DISPERSION (WAVES);

EID: 79961030338     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.04.008     Document Type: Article

References (27)

1. Swift J., Hohenberg P.C. Hydrodynamic fluctuations at the convective instability. Phys Rev A 1977, 15:319-328.
2. Aranson I.S., Gorshkov K.A., Lomov A.S., Rabinovich M.I. Stable particle-like solutions of multidimensional nonlinear fields. Phys D 1990, 43:435-453.
3. Pomeau Y., Zaleski S. Dislocation motion in cellular structures. J Phys 1981, 42:2710-2726.
4. Glebsky L.Yu., Lerman L.M. On small stationary localized solutions for the generalized 1-D Swift-Hohenberg equation. CHAOS 1995, 5:424-431.
5. Burke J., Houghton S.M., Knobloch E. Swift-Hohenberg equation with broken reflection symmetry. Phys Rev E 2009, 80. 036202.
6. Demina M.V., Kudryashov N.A. Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations. Commun Nonlinear Sci Numer Simulat 2011, 16:1127-1134.
7. Demina M.V., Kudryashov N.A. From Laurent series to exact meromorphic solutions: The Kawahara equation. Phys Lett A 2010, 374:4023-4029.
8. Kudryashov N.A. Exact soliton solutions of the generalized evolution equation of wave dynamics. J Appl Math Mech 1988, 52:361-365.
9. Kudryashov N.A. Exact solutions of the generalized Kuramoto-Sivashinsky equation. Phys Lett A 1990, 147:287-291.
10. Kudryashov N.A. Exact solutions of the non-linear wave equations arising in mechanics. J Appl Math Mech 1990, 54:372-375.
11. Kudryashov N.A. Partial differential equations with solutions having movable first - order singularities. Phys Lett A 1992, 169:237-242.
12. Parkes E.J., Duffy B.R. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Comput Phys Commun 1996, 98:288-300.
13. Fan E. Extended tanh-function method and its applications to nonlinear equations. Phys Lett A 2000, 277:212-218.
14. Fu Z., Liu S., Liu S. New transformations and new approach to find exact solutions to nonlinear equations. Phys Lett A 2002, 299:507-512.
15. Parkes E.J., Duffy B.R., Abbott P.C. The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations. Phys Lett A 2002, 295:280-286.
16. Kudryashov N.A. Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Soliton Fract 2005, 24:1217-1231.
17. Polyanin A.D., Zaitsev V.F., Zhyrov A.I. Methods of nonlinear equations of mathematical physics and mechanics 2005, Fizmatlit, Moscow, 260 P.
18. Vernov S.Yu. Proof of the absence of elliptic solutions of the cubic complex Ginzburg-Landau equation. Theor Math Phys 2006, 146:131-139.
19. Biswas A. Solitary wave solution for the generalized Kawahara equation. Appl Math Lett 2009, 22:208-210.
20. Kudryashov N.A., Loguinova N.B. Extended simplest equation method for nonlinear differential equations. Appl Math Comput 2008, 205:396-402.
21. Kudryashov N.A. Seven common errors in finding exact solutions of nonlinear differential equations. Commun Nonlinear Sci Numer Simulat 2009, 14:3507-3529.
22. Vitanov N.K. Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity. Commun Nonlinear Sci Numer Simulat 2010, 15:2050-2060.
23. Kudryashov N.A. Meromorphic solutions of nonlinear ordinary differential equations. Commun Nonlinear Sci Numer Simulat 2010, 15:2778-2790.
24. Kudryashov N.A., Sinelshchikov D.I., Demina M.V. Exact solutions of the generalized Bretherton equation. Phys Lett A 2011, 375:1074-1079.
25. Abramowitz M., Stegun I.A. Handbook of mathematical functions: with formulas, graphs and mathematical tables 1965, Dover Publications, 1046 P.
26. Cox S.M., Matthews P.C. Exponential time differencing for stiff systems. J Comput Phys 2002, 176:430-455.
27. Kassam A., Trefethen L.N. Fourth-order time stepping for stiff PDEs. SIAM J Sci Comput 2005, 26:1214-1233.