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Variational approach to the Benjamin Ono equation. (English) Zbl 1168.35304
Summary: Solitary solutions of the Benjamin Ono equation are studied via He’s variational method; the condition for existence of the solitary solutions is obtained.

35A25Other special methods (PDE)
35Q51Soliton-like equations
35A15Variational methods (PDE)
Full Text: DOI
[1] Mari, M.: On the existence, regularity and decay of solitary waves to a generalized benjamin--ono equation. Nonlinear anal. 51, 1073-1085 (2002) · Zbl 1082.35135
[2] Wu, X. H.; He, J. H.: Solitary solutions, periodic solutions and compacton-like solutions using the exp-function method. Comput. math. Appl. 54, 966-986 (2007) · Zbl 1143.35360
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[6] Yusufoglu, E.: Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations. Int. J. Nonlinear sci. 8, 153-158 (2007)
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[10] He, J. H.: New interpretation of homotopy perturbation method. Internat J. Modern phys. B 20, 2561-2568 (2006)
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[14] Ganji, D. D.; Sadighi, A.: Application of he’s homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations. Int. J. Nonlinear sci. 7, 411-418 (2006)
[15] He, J. H.; Wu, X. H.: Exp-function method for nonlinear wave equations. Chaos solitons fractals 30, 700-708 (2006) · Zbl 1141.35448
[16] Zhu, S. D.: Exp-function method for the hybrid-lattice system. Int. J. Nonlinear sci. 8, 461-464 (2007)
[17] Zhu, S. D.: Exp-function method for the discrete mkdv lattice. Int. J. Nonlinear sci. 8, 465-468 (2007)
[18] Bekir, A.; Boz, A.: Exact solutions for a class of nonlinear partial differential equations using exp-function method. Int. J. Nonlinear sci. 8, 505-512 (2007)
[19] He, J. H.: Some asymptotic methods for strongly nonlinear equations. Internat J. Modern phys. B 20, No. 10, 1141-1199 (2006) · Zbl 1102.34039
[20] J.H. He, Non-perturbative methods for strongly nonlinear problems, Berlin: dissertation.de-Verlag im Internet GmbH, 2006
[21] He, J. H.: Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos solitons fractals 19, No. 4, 847-851 (2004) · Zbl 1135.35303
[22] Tao, Z. L.: Variational approach to the inviscid compressible fluid. Acta appl. Math. 100, 291-294 (2008) · Zbl 1135.35305
[23] D’acunto, M.: Determination of limit cycles for a modified van der Pol oscillator. Mech. res. Commun. 33, No. 1, 93-98 (2006)
[24] D’acunto, M.: Self-excited systems: analytical determination of limit cycles. Chaos solitons fractals 30, No. 3, 719-724 (2006) · Zbl 1142.70010
[25] Öziş, T.; Yıldırım, A.: Application of he’s semi-inverse method to the nonlinear Schrödinger equation. Comput. math. Appl. 54, 1039-1042 (2007) · Zbl 1157.65465
[26] Zhang, J.: Variational approach to solitary wave solution of the generalized Zakharov equation. Comput. math. Appl. 54, 1043-1046 (2007) · Zbl 1141.65391