Variational principle for nonlinear Schrödinger equation with high nonlinearity
Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 1, p. 1-4.

Voir la notice de l'article provenant de la source International Scientific Research Publications

It is well-known that the Schrödinger equation plays an important role in physics and applied mathematics as well. Variational formulations have been one of the hottest topics. This paper suggests a simple but effective method called the semi-inverse method proposed by Ji-Huan He to construct a variational principle for the nonlinear Schrödinger equation with high nonlinearity.
DOI : 10.22436/jnsa.001.01.01
Classification : 58E30, 35A15, 34G20
Keywords: Variational principle, Semi-inverse method, nonlinear Schrödinger equation

Yao, Li 1 ; Chang, Jin-Rong 1

1 Department of Mathematics, Kunming College, Kunming,Yunnan, 650031, P.R. China
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Yao,  Li; Chang, Jin-Rong. Variational principle for nonlinear Schrödinger equation with high nonlinearity. Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 1, p. 1-4. doi : 10.22436/jnsa.001.01.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.001.01.01/

[1] Bekir, A.; Boz, A. Exact solutions for a class of nonlinear partial differential equations using exp-function method, Int. J. Nonlinear Sci., Volume 8 (2007), pp. 505-512 | DOI

[2] Biazar, J.; Ghazvini, H. Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method, Phys. Lett. A, Volume 366 (2008), pp. 79-84 | DOI | Zbl

[3] Bildik, N.; A. Konuralp 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. , Volume 7 (2006), pp. 65-70 | DOI

[4] Gorji, M.; Ganji, D. D.; Soleimani, S. New application of He’s homotopy perturbation method, Int. J. Nonlinear Sci. , Volume 8 (2007), pp. 319-328 | DOI

[5] He, J. H. New interpretation of homotopy perturbation method, Int. J. Modern Phys., Volume 2006 (B 20), pp. 2561-2568 | DOI

[6] He, J. H. Variational iteration method - Some recent results and new interpretations, J. Comput. and Appl. Math., Volume 207 (2007), pp. 3-17 | Zbl | DOI

[7] He, J. H. Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos, Solitons, Fractals, Volume 19 (2004), pp. 847-851 | DOI

[8] He, J. H. Variational approach to (2+1)-dimensional dispersive long water equations, Phys. Lett. A , Volume 335 (2005), pp. 182-184 | Zbl | DOI

[9] He, J. H. Some Asymptotic Methods for Strongly Nonlinear Equations, Int. J. Modern Phys. , Volume B 20 (2006), pp. 1141-1199 | DOI

[10] He, J. H. Non-perturbative methods for strongly nonlinear problems, dissertation.de-Verlag im Internet GmbH, Berlin, 2006

[11] J. H. He New interpretation of homotopy perturbation method, Int. J. Modern Phys. , Volume B 20 (2006), pp. 2561-2568 | DOI

[12] He, J. H.; Wu, X. H. Variational iteration method: New development and applications, Comput. & Math. with Appl. , Volume 54 (2007), pp. 881-894 | Zbl | DOI

[13] He, J. H.; Wu, X. H. Construction of solitary solution and compacton-like solution by variational iteration method, Chaos Solitons, Fractals. , Volume 29 (2006), pp. 108-113 | DOI | Zbl

[14] He, J. H.; Wu, X. H. Exp-function method for nonlinear wave equations, Chaos Solitons, Fractals , Volume 30 (2006), pp. 700-708 | DOI

[15] Odibat, Z. M.; S. Momani Application of variational iteration method to Nonlinear differential equations of fractional order, Int. J. Nonlinear Sci. , Volume 7 (2006), pp. 27-34 | DOI

[16] Ozis, T.; A. Yidirim Application of He’s semi-inverse method to the nonlinear Schrodinger equation, Comput. & Math. with Appl., Volume 54 (2007), pp. 1039-1042 | Zbl | DOI

[17] Sadighi, A.; D. D. Ganji Analytic treatment of linear and nonlinear Schrodinger equations: A study with homotopy-perturbation and Adomian decomposition methods, Phys. Lett. A , Volume 372 (2008), pp. 465-469 | Zbl | DOI

[18] Sweilam, N. H. Variational iteration method for solving cubic nonlinear Schrödinger equation, J. of Comput. and Appl. Math., Volume 207 (2007), pp. 155-163 | Zbl | DOI

[19] Sweilam, N. H.; R. F. Al-Bar Variational iteration method for coupled nonlinear Schrodinger equations, Comput. & Math. with Appl. , Volume 54 (2007), pp. 993-999 | DOI

[20] Z. L. Tao Variational approach to the inviscid compressible fluid , Acta Appl. Math., Volume 100 (2008), pp. 291-294 | DOI

[21] Wu, X. H.; He, J. H. Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method, Comput. & Math. with Appl. , Volume 54 (2007), pp. 966-986 | Zbl | DOI

[22] L. Xu Variational principles for coupled nonlinear Schrödinger equations, Phys. Lett. A , Volume 359 ( 2006), pp. 627-629 | DOI

[23] J. Zhang Variational approach to solitary wave solution of the generalized Zakharov equation, Comput. & Math. with Appl., Volume 54 (2007), pp. 1043-1046 | Zbl | DOI

[24] X. W. Zhou Variational theory for physiological flow, Comput. & Math. with Appl., Volume 54 (2007), pp. 1000-1002 | DOI

[25] X. W. Zhou Variational approach to the Broer-Kaup-Kupershmidt equation, Phys. Lett. A , Volume 363 (2007), pp. 108-109 | Zbl | DOI

[26] Zhu, S. D. Exp-function method for the Hybrid-Lattice system, Int. J. Nonlinear Sci. , Volume 8 (2007), pp. 461-464 | DOI

[27] Zhu, S. D. Exp-function method for the discrete mKdV lattice, Int. J. Nonlinear Sci., Volume 8 (2007), pp. 465-468 | DOI

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