Application of homotopy perturbation method to nonlinear wave equations

Chaos, Solitons and Fractals

Volumn 26, Issue 3, 2005, Pages 695-700

  He, Ji Huan ^a  

^a DONGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

BACKLUND TRANSFORMATIONS; HOMOTOPY PERTURBATION METHODS; INVERSE SCATTERING METHODS; NONLINEAR WAVE EQUATIONS;

WAVES;

EID: 18844426016     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.03.006     Document Type: Article

References (37)

1. S.-F. Deng Bäcklund transformation and soliton solutions for KP equation Chaos, Solitons & Fractals 25 2 2005 475 480
2. G. Tsigaridas, A. Fragos, I. Polyzos, and M. Fakis Evolution of near-soliton initial conditions in non-linear wave equations through their Bäcklund transforms Chaos, Solitons & Fractals 23 5 2005 1841 1854
3. O. Pashaev, and G. Tanoǧlu Vector shock soliton and the Hirota bilinear method Chaos, Solitons & Fractals 26 1 2005 95 105
4. V.O. Vakhnenko, E.J. Parkes, and A.J. Morrison A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation Chaos, Solitons & Fractals 17 4 2003 683 692
5. L. De-Sheng, G. Feng, and Z. Hong-Qing Solving the (2 + 1)-dimensional higher order Broer-Kaup system via a transformation and tanh-function method Chaos, Solitons & Fractals 20 5 2004 1021 1025
6. E.M.E. Zayed, H.A. Zedan, and K.A. Gepreel Group analysis and modified extended tanh-function to find the invariant solutions and soliton solutions for nonlinear Euler equations Int J Nonlinear Sci Numer Simul 5 3 2004 221 234
7. H.A. Abdusalam On an improved complex tanh-function method Int J Nonlinear Sci Numer Simul 6 2 2005 99 106
8. T.A. Abassy, M.A. El-Tawil, and H.K. Saleh The solution of KdV and mKdV equations using adomian pade approximation Int J Nonlinear Sci Numer Simul 5 4 2004 327 340
9. S.M. El-Sayed The decomposition method for studying the Klein-Gordon equation Chaos, Solitons & Fractals 18 5 2003 1025 1030
10. D. Kaya, and S.M. El-Sayed An application of the decomposition method for the generalized KdV and RLW equations Chaos, Solitons & Fractals 17 5 2003 869 877
11. H.M. Liu Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method Chaos, Solitons & Fractals 23 2 2005 573 576
12. H.M. Liu Variational approach to nonlinear electrochemical system Int J Nonlinear Sci Numer Simul 5 1 2004 95 96
13. J.H. He Variational principles for some nonlinear partial differential equations with variable coefficients Chaos, Solitons & Fractals 19 4 2004 847 851
14. A.M. Mesón, and F. Vericat Variational analysis for the multifractal spectra of local entropies and Lyapunov exponents Chaos, Solitons & Fractals 19 5 2004 1031 1038
15. J.H. He Variational iteration method: a kind of nonlinear analytical technique: some examples Int J Nonlinear Mech 34 4 1999 699 708
16. Gh.-E. Drǎgǎnescu, and V. Cǎpǎlnǎşan Polycrystalline solids, nonlinear relaxation phenomena in polycrystalline solids Int J Nonlinear Sci Numer Simul 4 3 2004 219 226
17. J.H. He Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part I: expansion of a constant Int J Nonlinear Mech 37 2 2002 309 314
18. J.H. He Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part II: a new transformation Int J Nonlinear Mech 37 2 2002 315 320
19. J.H. He Modified Lindstedt-Poincare methods for some strongly nonlinear oscillations. Part III: double series expansion Int J Nonlinear Sci Numer Simul 2 4 2001 317 320
20. H.M. Liu Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method Chaos, Solitons & Fractals 23 2005 577 579
21. J.H. He Gongcheng Yu Kexue zhong de jinshi feixianxing feixi fangfa (in Chinese) Asymptotic methods in engineering and sciences, or approximate analytical methods in engineering and sciences 2002 Henan Science and Technology Press Zhengzhou
22. J.H. He Determination of limit cycles for strongly nonlinear oscillators Phys Rev Lett 90 17 2003 174301
23. J. Shen, and W. Xu Bifurcations of smooth and non-smooth travelling wave solutions of the Degasperis-Procesi equation Int J Nonlinear Sci Numer Simul 5 4 2004 397 402
24. S. Ma, and Q. Lu Dynamical bifurcation for a predator-prey metapopulation model with delay Int J Nonlinear Sci Numer Simul 6 1 2005 13 18
25. Y. Zhang, and J. Xu Classification and computation of non-resonant double hopf bifurcations and solutions in delayed van der Pol-Duffing system Int J Nonlinear Sci Numer Simul 6 1 2005 63 68
26. Z. Zhang, and Q. Bi Bifurcations of a generalized Camassa-Holm equation Int J Nonlinear Sci Numer Simul 6 1 2005 81 86
27. Y. Zheng, and Y. Fu Effect of damage on bifurcation and chaos of viscoelastic plates Int J Nonlinear Sci Numer Simul 6 1 2005 87 91
28. S.I. Nada The effect of folding on covering spaces, immersions and bifurcation for chaotic manifolds Int J Nonlinear Sci Numer Simul 6 2 2005 145 150
29. J.H. He Homotopy perturbation technique Comp Meth Appl Mech Eng 178 1999 257 262
30. J.H. He A coupling method of homotopy technique and perturbation technique for nonlinear problems Int J Nonlinear Mech 35 2000 37 43
31. J.H. He Homotopy perturbation method for bifurcation of nonlinear problems Int J Nonlinear Sci Numer Simul 6 2 2005 207 208
32. Y. Yao Abundant families of new traveling wave solutions for the coupled Drinfel'd-Sokolov-Wilson equation Chaos, Solitons & Fractals 24 2005 301 307
33. M. El-Shahed Application of He's homotopy perturbation method to Volterra's integro-differential equation Int J Nonlinear Sci Numer Simul 6 2 2005 163 168
34. J.H. He Int J Nonlinear Sci Numer Simul 4 3 2003 313 314
35. T.H. Hao Int J Nonlinear Sci Numer Simul 4 3 2003 311 312
36. J.H. He Preliminary report on the energy balance for nonlinear oscillations Mech Res Commun 29 2-3 2002 107 111
37. Z. Fu, S. Liu, and S. Liu Multiple structures of 2-D nonlinear Rossby wave Chaos, Solitons & Fractals 24 2005 383 390