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Exact solution for nonlinear Schrödinger equation by He’s frequency formulation. (English) Zbl 1189.81064
Summary: We apply He’s frequency formulation to search for the solution to nonlinear Schrödinger equation. Three examples are given and the solutions obtained are in good accordance with A.-M. Wazwaz’s solution [A study on linear and nonlinear Schrodinger equations by the variational iteration method, Chaos Solitons Fractals 37, No. 4, 1136–1142 (2008)]. It is shown that He’s frequency formulation is of utter straightforward and effective.
MSC:
81Q05Closed and approximate solutions to quantum-mechanical equations
35Q55NLS-like (nonlinear Schrödinger) equations
References:
[1]Gao, Y. T.; Tian, B.: Internat. J. Modern phys. C, Internat. J. Modern phys. C 12, 197 (2001)
[2]Khater, A. H.; Callebaut, D. K.; Ibrahim, R. S.: Phys. plasmas, Phys. plasmas 5, 395 (1998)
[3]Sun, W. P.; Wu, B. S.; Lim, C. W.: J. sound vib., J. sound vib. 300, No. 5–6, 1042 (2007)
[4]Xu, L.: Phys. lett. A, Phys. lett. A 359, No. 6, 627 (2006)
[5]Xu, L.: Variational approach to solitons of nonlinear dispersive K(m,n) equations, Chaos solitons fractals 37, No. 1, 137-143 (2008) · Zbl 1143.35361 · doi:10.1016/j.chaos.2006.08.016
[6]He, J. H.: Variational iteration method – some recent results and new interpretations, J. comput. Appl. math. 207, No. 1, 3 (2007) · Zbl 1119.65049 · doi:10.1016/j.cam.2006.07.009
[7]He, J. H.; Wu, X. H.: Chaos solitons fractals, Chaos solitons fractals 29, No. 1, 108 (2006)
[8]Abdou, M. A.; Soliman, A. A.: Physica D, Physica D 211, No. 1–2, 1 (2005)
[9]Odibat, Z. M.; Momani, S.: Int. J. Nonlinear sci. Numer. simul., Int. J. Nonlinear sci. Numer. simul. 7, No. 1, 27 (2006)
[10]Momani, S.; Abuasad, S.: Chaos solitons fractals, Chaos solitons fractals 27, No. 5, 1119 (2006)
[11]He, J. H.: Phys. lett. A, Phys. lett. A 350, No. 1–2, 87 (2006)
[12]He, J. H.: Chaos solitons fractals, Chaos solitons fractals 26, No. 3, 695 (2005)
[13]He, J. H.: Int. J. Nonlinear sci. Numer. simul., Int. J. Nonlinear sci. Numer. simul. 6, No. 2, 207 (2005)
[14]He, J. H.: Internat. J. Modern phys. B, Internat. J. Modern phys. B 20, No. 18, 2561 (2006)
[15]Cai, X. C.; Wu, W. Y.; Li, M. S.: Int. J. Nonlinear sci. Numer. simul., Int. J. Nonlinear sci. Numer. simul. 7, No. 1, 109 (2006)
[16]Ariel, P. D.; Hayat, T.; Asghar, S.: Int. J. Nonlinear sci. Numer. simul., Int. J. Nonlinear sci. Numer. simul. 7, No. 4, 399 (2006)
[17]Ganji, D. D.; Sadighi, A.: Int. J. Nonlinear sci. Numer. simul., Int. J. Nonlinear sci. Numer. simul. 7, No. 4, 411 (2006)
[18]Rafei, M.; Ganji, D. D.: Int. J. Nonlinear sci. Numer. simul., Int. J. Nonlinear sci. Numer. simul. 7, No. 3, 321 (2006)
[19]Siddiqui, A. M.; Mahmood, R.; Ghori, Q. K.: Int. J. Nonlinear sci. Numer. simul., Int. J. Nonlinear sci. Numer. simul. 7, No. 1, 7 (2006)
[20]He, J. H.: Phys. rev. Lett., Phys. rev. Lett. 90, No. 17, 174301 (2003)
[21]He, J. H.: Phys. rev. Lett., Phys. rev. Lett. 91, No. 19, 199902 (2003)
[22]D’acunto, M.: Mech. res. Commun., Mech. res. Commun. 33, No. 1, 93 (2006)
[23]D’acunto, M.: Chaos solitons fractals, Chaos solitons fractals 30, No. 3, 719 (2006)
[24]He, J. -H.; Andwu, X. -H.: Exp-function method for nonlinear wave equations, Chaos solitons fractals 30, 700-708 (2006) · Zbl 1141.35448 · doi:10.1016/j.chaos.2006.03.020
[25]He, Ji-Huan; Zhang, Li-Na: Generalized solitary solution and compacton-like solution of the Jaulent–Miodek equations using the exp-function method, Phys. lett. A 372, No. 7, 1044-1047 (2008) · Zbl 1217.35152 · doi:10.1016/j.physleta.2007.08.059
[26]He, Ji-Huan; Abdou, M. A.: New periodic solutions for nonlinear evolution equations using exp-function method, Chaos solitons fractals 34, No. 5, 1421-1429 (2007) · Zbl 1152.35441 · doi:10.1016/j.chaos.2006.05.072
[27]Xu, Fei: Application of exp-function method to symmetric regularized long wave (SRLW) equation, Phys. lett. A 372, No. 3, 252-257 (2008) · Zbl 1217.35110 · doi:10.1016/j.physleta.2007.07.035
[28]Xu, Fei: Z. naturforsch., Z. naturforsch. 62a, 685-688 (2007)
[29]He, J. H.: Some asymptotic methods for strongly nonlinear equations, Internat. J. Modern phys. B 20, 1141-1199 (2006) · Zbl 1102.34039 · doi:10.1142/S0217979206033796
[30]He, J. H.: Comment on ’he’s frequency formulation for nonlinear oscillators’, Eur. J. Phys. 29, L1-L4 (2008)
[31]He, Ji-Huan: An improved amplitude-frequency formulation for nonlinear oscillators, Int. J. Nonlinear sci. Numer. simul. 9, No. 2, 211-212 (2008)
[32]J.H. He, 2006, Nonperturbative methods for strongly nonlinear problems, Dissertation, de-Verlag im Internet GmbH
[33]Wazwaz, Abdul-Majid: A study on linear and nonlinear Schrödinger equations by the variational iteration method, Chaos solitons fractals 37, No. 4, 1136-1142 (2008) · Zbl 1148.35353 · doi:10.1016/j.chaos.2006.10.009