Variational approach to the Benjamin Ono equation. (English) Zbl 1168.35304

Tao, Zhao-Ling

Nonlinear Anal., Real World Appl. 10, No. 3, 1939-1941 (2009).

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.

MSC:

35A25	Other special methods applied to PDEs
35Q51	Soliton equations
35A15	Variational methods applied to PDEs

Keywords:

He’s semi-inverse method; variational principle; Benjamin Ono equation

References:

[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
[3]	He, J. H., Variational iteration method — Some recent results and new interpretations, J. Comput. Appl. Math., 207, 3-17 (2007) · Zbl 1119.65049
[4]	Ozer, H., Application of the variational iteration method to the boundary value problems with jump discontinuities arising in solid mechanics, Int. J. Nonlinear Sci., 8, 513-518 (2007)
[5]	Tari, H.; Ganji, D. D.; Rostamian, M., Approximate solutions of K (2,2), KdV and modified KdV equations by variational iteration method, homotopy perturbation method and homotopy analysis method, Int. J. Nonlinear Sci., 8, 203-210 (2007)
[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)
[7]	Biazar, J.; Ghazvini, H., Title: He’s variational iteration method for solving hyperbolic differential equations, Int. J. Nonlinear Sci., 8, 311-314 (2007) · Zbl 1193.65144
[8]	Bildik, N.; Konuralp, A., The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations, Int. J. Nonlinear Sci., 7, 65-70 (2006) · Zbl 1401.35010
[9]	Odibat, Z. M.; Momani, S., Application of variational iteration method to Nonlinear differential equations of fractional order, Int. J. Nonlinear Sci., 7, 27-34 (2006) · Zbl 1401.65087
[10]	He, J. H., New interpretation of homotopy perturbation method, Internat J. Modern Phys. B, 20, 2561-2568 (2006)
[11]	Sadighi, A.; Ganji, D. D., Solution of the generalized nonlinear Boussinesq equation using homotopy perturbation and variational iteration methods, Int. J. Nonlinear Sci., 8, 435-443 (2007)
[12]	Shou, D. H.; He, J. H., Application of parameter-expanding method to strongly nonlinear oscillators, Int. J. Nonlinear Sci., 8, 121-124 (2007)
[13]	Gorji, M.; Ganji, D. D.; Soleimani, S., New application of He’s homotopy perturbation method, Int. J. Nonlinear Sci., 8, 319-328 (2007)
[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, 10, 1141-1199 (2006) · Zbl 1102.34039
[21]	He, J. H., Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos Solitons Fractals, 19, 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, 1, 93-98 (2006) · Zbl 1192.70026
[24]	D’Acunto, M., Self-excited systems: Analytical determination of limit cycles, Chaos Solitons Fractals, 30, 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