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Soliton solution to generalized nonlinear disturbed Klein-Gordon equation

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Abstract

A generalized nonlinear disturbed Klein-Gordon equation is studied. Using the homotopic mapping method, the corresponding homotopic mapping is constructed. A suitable initial approximation is selected, and an arbitrary-order approximate solution to the soliton is calculated. A weakly disturbed equation is also studied.

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References

  1. Ma, S. H., Qiang, J. Y., and Fang, J. P. The interaction between solitons and chaotic behaviours of (2+1)-dimensional Boiti-Leon-Pempinelli system (in Chinese). Acta Phys. Sin. 56, 620–626 (2007)

    MATH  MathSciNet  Google Scholar 

  2. Ma, S. H., Qiang, J. Y., and Fang, J. P. Annihilation solitons and chaotic solitons for the (2+1)-dimensional breaking soliton system. Commun. Theor. Phys. 48(4), 662–666 (2007)

    Article  MathSciNet  Google Scholar 

  3. Loutsenko, I. The variable coefficient Hele-Shaw problem, integrability and quadrature identities. Commun. Math. Phys. 268(2), 465–479 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. Gedalin, M. Low-frequency nonlinear stationary waves and fast shocks: hydrodynamical description. Phys. Plasmas 5(1), 127–132 (1998)

    Article  MathSciNet  Google Scholar 

  5. Parkes, E. J. Some periodic and solitary travelling-wave solutions of the short-pulse equation. Chaos, Solitons and Fractals 38(1), 154–159 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Li, X. Z., Li, X. Y., Zhang, L. Y., and Zhang, J. L. Exact solutions of Gerdjikov-Ivanov equation (in Chinese). Acta Phys. Sin. 57(4), 2231–2234 (2008)

    Google Scholar 

  7. Wang, M. L. Solitary wave solutions for variant Boussinesq equations. Phys. Lett. A 199(3–4), 169–172 (1995)

    Article  MathSciNet  Google Scholar 

  8. Sirendaoreji, and Jiong, S. Auxiliary equation method for solving nonlinear partial differential equations. Phys. Lett. A 309(5–6), 387–396 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. McPhaden, M. J. and Zhang, D. Slowdown of the meridional overturning circulation in the upper Pacific ocean. Nature 415(3), 603–608 (2002)

    Article  Google Scholar 

  10. Gu, D. F. and Philander, S. G. H. Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics. Science 275(7), 805–807 (1997)

    Article  Google Scholar 

  11. Pan, L. X., Zuo W., and Yan, J. R. The theory of the perturbation for Landau-Ginzburg-Higgs equation. Acta Phys. Sin. 54(1), 1–5 (1955)

    MathSciNet  Google Scholar 

  12. Ni, W. M. and Wei, J. C. On positive solution concentrating on spheres for the Gierer-Meinhardt system. Journal of Differential Equations 221(1), 158–189 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Bartier, J. P. Global behavior of solutions of a reaction-diffusion equation with gradient absorption in unbounded domains. Asymptotic Analysis 46(3–4), 325–347 (2006)

    MATH  MathSciNet  Google Scholar 

  14. Libre, J, da Silva, P. R., and Teixeira, M. A. Regularization of discontinuous vector fields on R3 via singular perturbation. Journal of Dynamics and Differential Equations 19(2), 309–331 (2007)

    Article  MathSciNet  Google Scholar 

  15. Guarguaglini, F. R. and Natalini, R. Fast reaction limit and large time behavior of solutions to a nonlinear model of sulphation phenomena. Communications in Partial Differential Equations 32(2), 163–189 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mo, J. Q. Approximate solution of homotopic mapping to solitary for generalized nonlinear KdV system. Chin. Phys. Lett. 26(1), 010204 (2009)

    Article  Google Scholar 

  17. Liao, S. J. Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Press Co., New York (2004)

    MATH  Google Scholar 

  18. Zheng, X. and Zhang, H. Q. Backlund transformation and exact solutions for (2+1)-dimensional Boussinesq equation. Acta Phys. Sin. 54(3), 1476–1480 (2005)

    Google Scholar 

  19. Ma, S. H., Fang, J. P., and Heng, C. L. Complex wave exitations and chaotic patterns for a general (2+1)-dimensional Korteweg-de Vries system. Chin. Phys. 17(8), 2767–2773 (2008)

    Article  Google Scholar 

  20. Liu, S. K., Fu, Z. T., Liu, S. D., and Zhao, Q. Expansion method about the Jacobi elliptic function and its applications tonnlinear wave equations. Acta Phys. Sin. 50(11), 2068–2073 (2001)

    MathSciNet  MATH  Google Scholar 

  21. De Jager, E. M. and Jiang, F. R. The Theory of Singular Perturbation, North-Holland Publishing Co., Amsterdam (1996)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Anhui Normal University, Wuhu, 241003, Anhui Province, P. R. China

    Jia-qi Mo  (莫嘉琪)

  2. Division of Computational Science, E-Institute of Shanghai Universities at SJTU, Shanghai, 200240, P. R. China

    Jia-qi Mo  (莫嘉琪)

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  1. Jia-qi Mo  (莫嘉琪)
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Correspondence to Jia-qi Mo  (莫嘉琪).

Additional information

Project supported by the National Natural Science Foundation of China (No. 40876010), the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences (No. KZCX2-YW-Q03-08), the Research and Development Special Fund for Public Welfare Industry (Meteorology) (No. GYHY200806010), the LASG State Key Laboratory Special Fund, and the Foundation of EInstitute of Shanghai Municipal Education Commission (No. E03004)

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Mo, Jq. Soliton solution to generalized nonlinear disturbed Klein-Gordon equation. Appl. Math. Mech.-Engl. Ed. 31, 1577–1584 (2010). https://doi.org/10.1007/s10483-010-1385-x

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  • DOI: https://doi.org/10.1007/s10483-010-1385-x

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