Traveling wave solutions of the generalized nonlinear evolution equations

Applied Mathematics and Computation

Volumn 210, Issue 2, 2009, Pages 551-557

  Kudryashov, Nikolai A ^a   Demina, Maria V ^a  

^a NATIONAL RESEARCH NUCLEAR UNIVERSITY MEPHI   (Russian Federation)

Author keywords

Nonlinear evolution equation; Simplest equation; Solitary wave solution; Traveling wave

Indexed keywords

DIFFERENTIAL EQUATIONS; LIQUID WAVES; WAVE EQUATIONS; WAVES;

NONLINEAR EVOLUTION EQUATION; SIMPLEST EQUATION; SOLITARY WAVE SOLUTION; TRAVELING WAVE; TRAVELING WAVE SOLUTIONS;

NONLINEAR EQUATIONS;

EID: 62949176122     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.11.048     Document Type: Article

References (33)

1. Korteweg D.J., and de Vries G. On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves. Philos. Mag. 39 (1895) 422-443
2. Zabuski N.J., and Kruskal M.D. Integration of "solitons" in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15 (1965) 240-242
3. Gardner C.S., Green J.M., Kruskal M.D., and Miura R.M. Method for solving the Korteweg-de Vries equations. Phys. Rev. Lett. 19 (1967) 1095-1097
4. Lax P.D. Integrals of nonlinear equations of evolution and solitary waves. Commun. Pure Appl. Math. 21 (1968) 467-490
5. Ablowitz M.J., and Clarkson P.A. Solitons Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge University Press
6. Kudryashov N.A. Analytical Theory of Nonlinear Differential Equations (2004), Institute of Computer Investigations, Moskow - Igevsk (in Russian)
7. Kuramoto Y., and Tsuzuki T. Persistent propagation of concentration waves in dissipative media far from thermal equilibrium. Prog. Theor. Phys. 52 2 (1976) 356-369
8. Benney D.J. Long waves on liquid films. J. Math. Phys. 45 (1966) 150
9. Topper J., and Kawahara T. Approximate equation for long nonlinear waves on a viscous fluid. J. Phys. Soc. Jpn. 44 (1978) 663-666
10. Shkadov V.Y. Solitary waves in layer of viscous fluid. Fluid Dynam. 1 (1977) 63-66
11. Cohen B.I., Krommers J.A., Tang W.M., and Rosenbluth M.N. Non-linear saturation of the dissipative trapped-ion mode by mode coupling. Nucl. Fusion 16 6 (1976) 971-992
12. Michelson D. Elementary particles as solutions of the Sivashinsky equation. Physica D 44 (1990) 502-556
13. Lu D., Hong B., and Tian L. New solitary wave and periodic wave solutions for general types of KdV and KdV-Burgers equations. Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 77-84
14. Peng Y.Z. Exact travelling wave solutions for the Zakharov-Kuznetsov equation. Appl. Math. Comput. 199 (2008) 397-405
15. Zhu Z.N. Exact solutions to two-dimensional generalized fifth order Kuramoto-Sivashinsky type equation. Chin. J. Phys. 84 2 (1996) 85-90
16. Qin M., and Fan G. An effective method for finding special solutions of nonlinear differential equations with variable coefficients. Phys. Lett. A 372 (2008) 3240-3242
17. Kudryashov N.A. Solitary and periodic solutions of the generalized Kuramoto-Sivashinsky equation. Regul. Chaotic Dynam. 13 3 (2008) 234-238
18. Kudryashov N.A. Exact soliton solutions of the generalized evolution equation of wave dynamics. J. Appl. Math. Mech. 52 3 (1988) 360-365
19. Conte R., and Museette M. Painleve analysis and Backlund transformation in the Kuramoto-Sivashinsky equation. J. Phys. A: Math. Gen. 22 (1989) 169-177
20. Kudryashov N.A. Exact solutions of the generalized Kuramoto-Sivashinsky equation. Phys. Lett. A 147 (1990) 287-291
21. Kudryashov N.A. On types of nonlinear nonintegrable equations with exact solutions. Phys. Lett. A 155 (1991) 269-275
22. Kudryashov N.A., and Zargaryan E.D. Solitary waves in active-dissipative dispersive media. J. Phys. A: Math. Gen. 29 (1996) 8067-8077
23. Berloff N.G., and Howard L.N. Solitary and periodic solutions of nonlinear nonintegrable equations. Stud. Appl. Math. 99 (1997) 1-24
24. Davalos-Orozco L.A., and Busse F.N. Instability of a thin film flowing on a rotating horizontal or inclined plane. Phys. Rev. E 65 (2002) 026312-2-026312-10
25. Fu S., Liu S., and Liu S. New exact solutions to the KdV-Burgers-Kuramoto equation. Chaos Solitons Fract. 23 (2005) 609-616
26. Zhang S. New exact solutions of the KdV-Burgers-Kuramoto equation. Phys. Lett. A 358 (2006) 414-420
27. Khuri S.A. Traveling wave solutions for nonlinear differential equations: a unified ansatse approach. Chaos Solitons Fract. 32 (2007) 252-258
28. Nickel J. Traveling wave solutions to the Kuramoto-Sivashinsky equation. Chaos Solitons Fract. 33 (2007) 1376-1382
29. Kudryashov N.A. Exact solitary waves of the Fisher equation. Phys. Lett. A 342 (2005) 99-106
30. Kudryashov N.A. Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fract. 24 (2005) 1217-1231
31. Kudryashov N.A., and Demina M.V. Polygons of differential equation for finding exact solutions. Chaos Solitons Fract. 33 (2007) 1480-1496
32. Kudryashov N.A., and Loguinova N.B. Extended simplest equation method for nonlinear differential equations. Appl. Math. Comput. 205 1 (2008) 396-402
33. Kudryashov N.A., and Loguinova N.B. Be careful with Exp-function method. Commun. Nonlinear Sci. Numer. Simul. (2008) 10.1016/j.cnsns.2008.07.021