메뉴 건너뛰기




Volumn 8, Issue 2, 2007, Pages 239-242

Traveling wave solution of Korteweg-de vries equation using He's Homotopy Perturbation Method

Author keywords

Homotopy perturbation method; KdV equations; Modified lindstedt poincar method

Indexed keywords


EID: 34249884542     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2007.8.2.239     Document Type: Article
Times cited : (120)

References (43)
  • 1
    • 36849100403 scopus 로고
    • Backlund transformations for certain nonlinear evolution equations
    • Lamb, G. L. Jr. Backlund transformations for certain nonlinear evolution equations, J. Math. Phys. 15: 2157-2165(1974)
    • (1974) J. Math. Phys , vol.15 , pp. 2157-2165
    • Lamb Jr., G.L.1
  • 3
    • 0000999098 scopus 로고
    • Hirota's method and the singular manifold expansion
    • Nozaki, K. Hirota's method and the singular manifold expansion, J. Phys. Soc. Jpn.,56: 3052-3054(1987)
    • (1987) J. Phys. Soc. Jpn , vol.56 , pp. 3052-3054
    • Nozaki, K.1
  • 5
    • 34249908176 scopus 로고    scopus 로고
    • Ablowitz, M.J. Segur.H. Solitons and Inverse Scattering Transform, SIAM Studies in Apllied Mathematics, 4, Philadelphia (1981)
    • Ablowitz, M.J. Segur.H. Solitons and Inverse Scattering Transform, SIAM Studies in Apllied Mathematics, Vol. 4, Philadelphia (1981)
  • 6
    • 0347985405 scopus 로고    scopus 로고
    • Solving the (2+1)- dimensional higher order Broer-Kaup system via a transformation and tanh-runction method
    • De-Sheng L., Feng G., Hong-Quing, Z., Solving the (2+1)- dimensional higher order Broer-Kaup system via a transformation and tanh-runction method, Chaos, Solitons & Fractals, 20:1021-5 (2004)
    • (2004) Chaos, Solitons & Fractals , vol.20 , pp. 1021-1025
    • De-Sheng, L.1    Feng, G.2    Hong-Quing, Z.3
  • 8
    • 0041185368 scopus 로고
    • A review of the decomposition method in applied mathematics
    • Adomian, G. A review of the decomposition method in applied mathematics, J Math. Anal & Appl., 135:501-544 (1988)
    • (1988) J Math. Anal & Appl , vol.135 , pp. 501-544
    • Adomian, G.1
  • 10
    • 0003083585 scopus 로고
    • A reliable modification of adomian's decomposition method
    • Wazwaz, A.M. A reliable modification of adomian's decomposition method, Appl. Math. Comput.,92: 1-7 (1988)
    • (1988) Appl. Math. Comput , vol.92 , pp. 1-7
    • Wazwaz, A.M.1
  • 11
    • 0038577058 scopus 로고    scopus 로고
    • The decomposition method for studying the Klein-Gordon equation
    • El-Sayed, SM. The decomposition method for studying the Klein-Gordon equation, Chaos, Solitons & Fractals 18: 1025-1030 (2003)
    • (2003) Chaos, Solitons & Fractals , vol.18 , pp. 1025-1030
    • El-Sayed, S.M.1
  • 12
    • 4243080806 scopus 로고    scopus 로고
    • Generalized variational principles for ion acoustic plasma waves by He's semiinverse method
    • Liu, HM. Generalized variational principles for ion acoustic plasma waves by He's semiinverse method, Chaos, Solitons Fractals 23: 573-576(2005)
    • (2005) Chaos, Solitons Fractals , vol.23 , pp. 573-576
    • Liu, H.M.1
  • 13
    • 0041621600 scopus 로고    scopus 로고
    • Variational principles for some nonlinear partial differential equations with variable coefficients
    • He, JH. Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos, Solitons Fractals 19: 847-851 (2004)
    • (2004) Chaos, Solitons Fractals , vol.19 , pp. 847-851
    • He, J.H.1
  • 14
    • 0031441505 scopus 로고    scopus 로고
    • Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics
    • He, JH. Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics, Int. J. Turbo Jet-Engines, 14: 23-28(1997)
    • (1997) Int. J. Turbo Jet-Engines , vol.14 , pp. 23-28
    • He, J.H.1
  • 15
    • 34249872810 scopus 로고    scopus 로고
    • An application of He's semi-inverse method to the nonlinear Schrödinger (NLS) equation
    • accepted
    • Öziş, T., Yildirim, A. An application of He's semi-inverse method to the nonlinear Schrödinger (NLS) equation, Computers and Mathematics with Applications (accepted)
    • Computers and Mathematics with Applications
    • Öziş, T.1    Yildirim, A.2
  • 16
    • 34748902823 scopus 로고    scopus 로고
    • Determination of frequency-amplitude relation for Duffing-Harmonic Oscillator by the Energy Balance Method
    • accepted
    • Öziş, T., Yildirim, A. Determination of frequency-amplitude relation for Duffing-Harmonic Oscillator by the Energy Balance Method, Computers and Mathematics with Applications (accepted)
    • Computers and Mathematics with Applications
    • Öziş, T.1    Yildirim, A.2
  • 17
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration method: A kind of nonlinear analytical technique: some examples
    • He, JH. Variational iteration method: a kind of nonlinear analytical technique: some examples, International Journal of Non-linear mechanics, 34 :699-708(1999)
    • (1999) International Journal of Non-linear mechanics , vol.34 , pp. 699-708
    • He, J.H.1
  • 18
    • 0040184009 scopus 로고    scopus 로고
    • Variational iteration method for authonomus ordinary differential systems
    • He, JH. Variational iteration method for authonomus ordinary differential systems, Appl. Math. Comput. 114: 115-123 (2000)
    • (2000) Appl. Math. Comput , vol.114 , pp. 115-123
    • He, J.H.1
  • 19
    • 34250668369 scopus 로고    scopus 로고
    • Variational iteration method- Some recent results and new interpretations
    • in press
    • He, JH. Variational iteration method- Some recent results and new interpretations, Journal of Computational and Applied Mathematics, (in press)
    • Journal of Computational and Applied Mathematics
    • He, J.H.1
  • 22
    • 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, 26: 695-700(2005)
    • (2005) Chaos, Solitons and Fractals , vol.26 , pp. 695-700
    • He, J.H.1
  • 23
    • 34249869084 scopus 로고    scopus 로고
    • A Coupled Method of He's Homotopy Perturbation Method and Modified Lindstedt-Poincaré Method for Traveling Wave Solutions of the Nonlinear Klein-Gordon Equation
    • submitted
    • Öziş, T. Yildirim, A. A Coupled Method of He's Homotopy Perturbation Method and Modified Lindstedt-Poincaré Method for Traveling Wave Solutions of the Nonlinear Klein-Gordon Equation, J. of Franklin Institute (2007) (submitted)
    • (2007) J. of Franklin Institute
    • Öziş, T.1    Yildirim, A.2
  • 25
    • 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 35: 37-43(2000)
    • (2000) International Journal of Non-linear Mechanics , vol.35 , pp. 37-43
    • He, J.H.1
  • 26
    • 17844395724 scopus 로고    scopus 로고
    • Application of He's Homotopy Perturbation Method to Volterra's Integrodifferential Equation
    • El-Shahed M. Application of He's Homotopy Perturbation Method to Volterra's Integrodifferential Equation, International Journal of Nonlinear Sciences & Numerical Simulation 6:163-168(2005)
    • (2005) International Journal of Nonlinear Sciences & Numerical Simulation , vol.6 , pp. 163-168
    • El-Shahed, M.1
  • 27
    • 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 & Fractals, 26: 695-700(2005)
    • (2005) Chaos Solitons & Fractals , vol.26 , pp. 695-700
    • He, J.H.1
  • 29
    • 4344696077 scopus 로고    scopus 로고
    • Asymptotology by homotopy perturbation method
    • He, JH. Asymptotology by homotopy perturbation method, Applied Mathematics and Computation, 156: 591-596(2004)
    • (2004) Applied Mathematics and Computation , vol.156 , pp. 591-596
    • He, J.H.1
  • 30
    • 1242287587 scopus 로고    scopus 로고
    • The homotopy perturbation method for nonlinear oscillators with discontinuities
    • He, JH. The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied Mathematics and Computation, 151 : 287-292(2004)
    • (2004) Applied Mathematics and Computation , vol.151 , pp. 287-292
    • He, J.H.1
  • 31
    • 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, 135: 73-79 (2003)
    • (2003) Applied Mathematics and Computation , vol.135 , pp. 73-79
    • He, J.H.1
  • 32
    • 34247154842 scopus 로고    scopus 로고
    • A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity
    • doi:10.1016/j.chaos.2006.04.013
    • Öziş, T., Yildirim, A. A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity, Chaos Solitons & Fractals, doi:10.1016/j.chaos.2006.04.013
    • Chaos Solitons & Fractals
    • Öziş, T.1    Yildirim, A.2
  • 33
    • 0036489498 scopus 로고    scopus 로고
    • Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part I: Expansion of a constant
    • He, J.H. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part I: expansion of a constant. Int. J. Nonlinear Mech., 37: 309-314(2002)
    • (2002) Int. J. Nonlinear Mech , vol.37 , pp. 309-314
    • He, J.H.1
  • 34
    • 0036489502 scopus 로고    scopus 로고
    • Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part II: A new transformation
    • He, J.H. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part II: a new transformation, Int. J. Nonlinear Mech., 37: 315-320(2002)
    • (2002) Int. J. Nonlinear Mech , vol.37 , pp. 315-320
    • He, J.H.1
  • 35
    • 0035603591 scopus 로고    scopus 로고
    • Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part III: Double series expansion
    • He, JH. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part III: double series expansion. Int J. Nonlinear Sci. Numer. Simul. 2: 317-320(2001)
    • (2001) Int J. Nonlinear Sci. Numer. Simul , vol.2 , pp. 317-320
    • He, J.H.1
  • 36
    • 4243080805 scopus 로고    scopus 로고
    • Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method
    • Liu, HM. Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method, Chaos, Solitons & Fractals, 23: 577-579(2005)
    • (2005) Chaos, Solitons & Fractals , vol.23 , pp. 577-579
    • Liu, H.M.1
  • 37
    • 33749550434 scopus 로고    scopus 로고
    • Determination of limit cycles by Modified Straightforward expansion for nonlinear oscillators
    • Öziş, T.,Yildirim, A. Determination of limit cycles by Modified Straightforward expansion for nonlinear oscillators, Chaos, Solitons & Fractals, 32: 445-448 (2007)
    • (2007) Chaos, Solitons & Fractals , vol.32 , pp. 445-448
    • Öziş, T.1    Yildirim, A.2
  • 39
    • 41849137278 scopus 로고    scopus 로고
    • Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation
    • doi:10.1016/j.chaos.2006.11.006
    • Öziş, T., Yildirim, A., Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation, Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2006.11.006
    • Chaos, Solitons & Fractals
    • Öziş, T.1    Yildirim, A.2
  • 40
    • 34249889124 scopus 로고    scopus 로고
    • He, J.H. Non-Perturbative Methods for Strongly Nonlinear Problems, dissertation.deVerlag im Internet GmbH, 2006
    • He, J.H. Non-Perturbative Methods for Strongly Nonlinear Problems, dissertation.deVerlag im Internet GmbH, 2006
  • 41
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • He JH. Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B 20: 1141-1199(2006)
    • (2006) International Journal of Modern Physics B , vol.20 , pp. 1141-1199
    • He, J.H.1
  • 42
    • 33746584753 scopus 로고    scopus 로고
    • New interpretation of homotopy perturbation method
    • He, J.H. New interpretation of homotopy perturbation method, International Journal of Modern Physics B 20: 2561-2568(2006)
    • (2006) International Journal of Modern Physics B , vol.20 , pp. 2561-2568
    • He, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.