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Volumn 26, Issue 2, 2010, Pages 266-272

Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations

Author keywords

He's variational iteration method; Lagrange multiplier; Modified Camassa Holm and Degasperis Procesi equations; Nonlinear phenomena

Indexed keywords

COMPUTABLE COMPONENTS; CONVERGENT SERIES; DEGASPERIS-PROCESI EQUATIONS; HE'S VARIATIONAL ITERATION METHOD; NON-LINEAR PHENOMENA; NONLINEAR DIFFERENTIAL EQUATION; NONLINEAR DISPERSION; PERTURBATION THEORY; SCIENCE AND ENGINEERING; VARIATIONAL ITERATION METHOD; WEAK NONLINEARITY ASSUMPTIONS;

EID: 77649179144     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.1154     Document Type: Article
Times cited : (39)

References (45)
  • 1
    • 0037411678 scopus 로고    scopus 로고
    • A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation
    • Vakhnenko VO, Parkes EJA, Morrison AJ. A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. Chaos, Solitons and Fractals 2003; 17:683-692.
    • (2003) Chaos, Solitons and Fractals , vol.17 , pp. 683-692
    • Vakhnenko, V.O.1    Parkes, E.J.A.2    Morrison, A.J.3
  • 2
    • 0035452509 scopus 로고    scopus 로고
    • Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method
    • Wazwaz AM. Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method. Chaos, Solitons and Fractals 2001; 12:2283-2293.
    • (2001) Chaos, Solitons and Fractals , vol.12 , pp. 2283-2293
    • Wazwaz, A.M.1
  • 3
    • 34248208547 scopus 로고    scopus 로고
    • Solution of a semilinear parabolic equation with an unknown control function using the decomposition procedure of Adomian
    • Dehghan M, Tatari M. Solution of a semilinear parabolic equation with an unknown control function using the decomposition procedure of Adomian. Numerical Methods for Partial Differential Equations 2007; 23:499-510.
    • (2007) Numerical Methods for Partial Differential Equations , vol.23 , pp. 499-510
    • Dehghan, M.1    Tatari, M.2
  • 4
    • 46449132300 scopus 로고    scopus 로고
    • Comparison between Adomian's method and He's homotopy perturbation method
    • DOI: 10.1016/j.camwa.02.023
    • Öziş T, Yildirim A. Comparison between Adomian's method and He's homotopy perturbation method. Computer Mathematics with Applications 2008; DOI: 10.1016/j.camwa.02.023.
    • (2008) Computer Mathematics with Applications
    • Öziş, T.1    Yildirim, A.2
  • 5
    • 17644427366 scopus 로고    scopus 로고
    • Vector shock soliton and the Hirota bilinear method
    • Pashaev O, Tanoglu G. Vector shock soliton and the Hirota bilinear method. Chaos, Solitons and Fractals 2005; 26:95-105.
    • (2005) Chaos, Solitons and Fractals , vol.26 , pp. 95-105
    • Pashaev, O.1    Tanoglu, G.2
  • 6
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • He JH, Wu XH. Exp-function method for nonlinear wave equations. Chaos, Solitons and Fractals 2006; 30:700-708.
    • (2006) Chaos, Solitons and Fractals , vol.30 , pp. 700-708
    • He, J.H.1    Wu, X.H.2
  • 7
    • 0000615571 scopus 로고    scopus 로고
    • An approximate solution technique not depending on small parameters: a special example
    • Liao SJ. An approximate solution technique not depending on small parameters: a special example. International Journal of Non-linear Mechanics 1996; 30:371-380.
    • (1996) International Journal of Non-linear Mechanics , vol.30 , pp. 371-380
    • Liao, S.J.1
  • 9
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of a homotopy technique and a perturbation technique for non-linear problems
    • He JH. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. International Journal of Non-linear Mechanics 2000; 35:37-43.
    • (2000) International Journal of Non-linear Mechanics , vol.35 , pp. 37-43
    • He, J.H.1
  • 10
    • 0037440579 scopus 로고    scopus 로고
    • Homotopy perturbation method: a new nonlinear analytical technique
    • He JH. Homotopy perturbation method: a new nonlinear analytical technique. Applied Mathematics and Computation 2003; 135:73-79.
    • (2003) Applied Mathematics and Computation , vol.135 , pp. 73-79
    • He, J.H.1
  • 11
    • 1242287587 scopus 로고    scopus 로고
    • He's homotopy perturbation method for nonlinear oscillators with discontinuities
    • He JH. He's homotopy perturbation method for nonlinear oscillators with discontinuities. Applied Mathematics and Computation 2004; 151:287-292.
    • (2004) Applied Mathematics and Computation , vol.151 , pp. 287-292
    • He, J.H.1
  • 12
    • 18844426016 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to nonlinear wave equations
    • He JH. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons and Fractals 2005; 26:695-700.
    • (2005) Chaos, Solitons and Fractals , vol.26 , pp. 695-700
    • He, J.H.1
  • 13
    • 34247154842 scopus 로고    scopus 로고
    • A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity
    • Öziş T, Yildirim A. A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity. Chaos, Solitons and Fractals 2007; 34:989-991.
    • (2007) Chaos, Solitons and Fractals , vol.34 , pp. 989-991
    • Öziş, T.1    Yildirim, A.2
  • 15
    • 34249884541 scopus 로고    scopus 로고
    • A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities
    • Öziş T, Yildirim A. A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities. International Journal of Nonlinear Sciences and Numerical Simulation 2007; 8:243-248.
    • (2007) International Journal of Nonlinear Sciences and Numerical Simulation , vol.8 , pp. 243-248
    • Öziş, T.1    Yildirim, A.2
  • 16
    • 34548249064 scopus 로고    scopus 로고
    • Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method
    • Yildirim A, Öziş T. Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method. Physics Letters A 2007; 369:70-76.
    • (2007) Physics Letters A , vol.369 , pp. 70-76
    • Yildirim, A.1    Öziş, T.2
  • 17
    • 47049085208 scopus 로고    scopus 로고
    • Exact solutions of nonlinear differential-difference equations by He's homotopy perturbation method
    • Yildirim A. Exact solutions of nonlinear differential-difference equations by He's homotopy perturbation method. International Journal of Nonlinear Sciences and Numerical Simulation 2008; 9:111-114.
    • (2008) International Journal of Nonlinear Sciences and Numerical Simulation , vol.9 , pp. 111-114
    • Yildirim, A.1
  • 18
    • 77649111755 scopus 로고    scopus 로고
    • On the solution of the non-linear Korteweg-de Vries equation by the homotopy perturbation method
    • DOI: 10.1002/cnm.1146
    • Yildirim A. On the solution of the non-linear Korteweg-de Vries equation by the homotopy perturbation method. Communications in Numerical Methods in Engineering 2008; DOI: 10.1002/cnm.1146.
    • (2008) Communications in Numerical Methods in Engineering
    • Yildirim, A.1
  • 19
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration method-a kind of non-linear analytical technique: some examples
    • He JH. Variational iteration method-a kind of non-linear analytical technique: some examples. International Journal of Non-linear Mechanics 1999; 34:699-708.
    • (1999) International Journal of Non-linear Mechanics , vol.34 , pp. 699-708
    • He, J.H.1
  • 20
    • 0040184009 scopus 로고    scopus 로고
    • Variational iteration method for autonomous ordinary differential system
    • He JH. Variational iteration method for autonomous ordinary differential system. Applied Mathematics and Computation 2000; 114:115-123.
    • (2000) Applied Mathematics and Computation , vol.114 , pp. 115-123
    • He, J.H.1
  • 21
    • 30344475545 scopus 로고    scopus 로고
    • Construction of solitary solution and compaction-like solution by variational iteration method
    • He JH, Wu XH. Construction of solitary solution and compaction-like solution by variational iteration method. Chaos, Solitons and Fractals 2006; 29:108-113.
    • (2006) Chaos, Solitons and Fractals , vol.29 , pp. 108-113
    • He, J.H.1    Wu, X.H.2
  • 23
    • 59049085436 scopus 로고    scopus 로고
    • Solutions of singular IVPs of Lane-Emden type by the variational iteration method
    • DOI: 10.1016/j.na.2008.03.012
    • Yildirim A, Öziş T. Solutions of singular IVPs of Lane-Emden type by the variational iteration method. Nonlinear Analysis Series A: Theory, Methods and Applications 2008; DOI: 10.1016/j.na.2008.03.012.
    • (2008) Nonlinear Analysis Series A: Theory, Methods and Applications
    • Yildirim, A.1    Öziş, T.2
  • 24
    • 34748875886 scopus 로고    scopus 로고
    • The variational iteration method: a powerful scheme for handling linear and nonlinear diffusion equations
    • Wazwaz AM. The variational iteration method: a powerful scheme for handling linear and nonlinear diffusion equations. Computers and Mathematics with Applications 2007; 54:933-939.
    • (2007) Computers and Mathematics with Applications , vol.54 , pp. 933-939
    • Wazwaz, A.M.1
  • 26
    • 34748865368 scopus 로고    scopus 로고
    • Exact solutions of nonlinear diffusion equations by variational iteration method
    • Sadighi A, Ganji DD. Exact solutions of nonlinear diffusion equations by variational iteration method. Computers and Mathematics with Applications 2007; 54:1112-1121.
    • (2007) Computers and Mathematics with Applications , vol.54 , pp. 1112-1121
    • Sadighi, A.1    Ganji, D.D.2
  • 27
    • 34848910713 scopus 로고    scopus 로고
    • A variational iteration method for solving parabolic partial differential equations
    • Golbabai A, Javidi M. A variational iteration method for solving parabolic partial differential equations. Computers and Mathematics with Applications 2007; 54:987-992.
    • (2007) Computers and Mathematics with Applications , vol.54 , pp. 987-992
    • Golbabai, A.1    Javidi, M.2
  • 28
    • 33846523615 scopus 로고    scopus 로고
    • Solution of problems in calculus of variations via He's variational iteration method
    • Tatari M, Dehghan M. Solution of problems in calculus of variations via He's variational iteration method. Physics Letters A 2007; 362:401-406.
    • (2007) Physics Letters A , vol.362 , pp. 401-406
    • Tatari, M.1    Dehghan, M.2
  • 29
    • 33749530855 scopus 로고    scopus 로고
    • The use of He's variational iteration method for solving a Fokker-Planck equation
    • Dehghan M, Tatari M. The use of He's variational iteration method for solving a Fokker-Planck equation. Physica Scripta 2006; 74:310-316.
    • (2006) Physica Scripta , vol.74 , pp. 310-316
    • Dehghan, M.1    Tatari, M.2
  • 30
    • 35348829740 scopus 로고    scopus 로고
    • Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method
    • Dehghan M, Tatari M. Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method. Chaos, Solitons and Fractals 2008; 36:157-166.
    • (2008) Chaos, Solitons and Fractals , vol.36 , pp. 157-166
    • Dehghan, M.1    Tatari, M.2
  • 31
    • 33847215123 scopus 로고    scopus 로고
    • He's variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation
    • Tatari M, Dehghan M. He's variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation. Chaos, Solitons and Fractals 2007; 33:671-677.
    • (2007) Chaos, Solitons and Fractals , vol.33 , pp. 671-677
    • Tatari, M.1    Dehghan, M.2
  • 32
    • 35448960877 scopus 로고    scopus 로고
    • Numerical solution of the Klein-Gordon equation via He's variational iteration method
    • Shakeri F, Dehghan M. Numerical solution of the Klein-Gordon equation via He's variational iteration method. Nonlinear Dynamics 2008; 51:89-97.
    • (2008) Nonlinear Dynamics , vol.51 , pp. 89-97
    • Shakeri, F.1    Dehghan, M.2
  • 33
    • 34848823089 scopus 로고    scopus 로고
    • Numerical solution of a biological population model using He's variational iteration method
    • Shakeri F, Dehghan M. Numerical solution of a biological population model using He's variational iteration method. Computers and Mathematics with Applications 2007; 54:1197-1209.
    • (2007) Computers and Mathematics with Applications , vol.54 , pp. 1197-1209
    • Shakeri, F.1    Dehghan, M.2
  • 34
    • 34548509029 scopus 로고    scopus 로고
    • Approximate solution of a differential equation arising in astrophysics using the variational iteration method
    • Dehghan M, Shakeri F. Approximate solution of a differential equation arising in astrophysics using the variational iteration method. New Astronomy 2008; 13:53-59.
    • (2008) New Astronomy , vol.13 , pp. 53-59
    • Dehghan, M.1    Shakeri, F.2
  • 35
    • 39149109311 scopus 로고    scopus 로고
    • Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem
    • Dehghan M, Shakeri F. Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem. Journal of Computational and Applied Mathematics 2008; 214:435-446.
    • (2008) Journal of Computational and Applied Mathematics , vol.214 , pp. 435-446
    • Dehghan, M.1    Shakeri, F.2
  • 37
    • 47949123722 scopus 로고    scopus 로고
    • Solution of a model describing biological species living together using the variational iteration method
    • DOI: 10.1016/j.mcm.2007.11.012
    • Shakeri F, Dehghan M. Solution of a model describing biological species living together using the variational iteration method. Mathematical and Computer Modelling 2007; DOI: 10.1016/j.mcm.2007.11.012.
    • (2007) Mathematical and Computer Modelling
    • Shakeri, F.1    Dehghan, M.2
  • 40
    • 20444495185 scopus 로고    scopus 로고
    • Time-accurate solution of advection-diffusion problems by wavelet-Taylor-Galerkin method
    • Mani M, Rathish Kumar BV. Time-accurate solution of advection-diffusion problems by wavelet-Taylor-Galerkin method. Communications in Numerical Methods in Engineering 2005; 21:313-326.
    • (2005) Communications in Numerical Methods in Engineering , vol.21 , pp. 313-326
    • Mani, M.1    Rathish Kumar, B.V.2
  • 44
    • 33644938250 scopus 로고    scopus 로고
    • Solitary wave solutions for modified forms of Degasperis-Procesi and Camassa-Holm equations
    • Wazwaz AM. Solitary wave solutions for modified forms of Degasperis-Procesi and Camassa-Holm equations. Physics Letters A 2006; 352:500-504.
    • (2006) Physics Letters A , vol.352 , pp. 500-504
    • Wazwaz, A.M.1
  • 45
    • 43049116900 scopus 로고    scopus 로고
    • Homotopy perturbation method for modified Camassa-Holm and Degasperis-Procesi equations
    • Zhang B, Li S, Liu Z. Homotopy perturbation method for modified Camassa-Holm and Degasperis-Procesi equations. Physics Letters A 2008; 372:1867-1872.
    • (2008) Physics Letters A , vol.372 , pp. 1867-1872
    • Zhang, B.1    Li, S.2    Liu, Z.3


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