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Exact Solutions of Fisher and Generalized Fisher Equations with Variable Coefficients

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Abstract

In this work, we consider a Fisher and generalized Fisher equations with variable coefficients. Using truncated Painlevé expansions of these equations, we obtain exact solutions of these equations with a constraint on the coefficients a(t) and b(t).

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References

  1. Ablowitz, M., Segur, H. Solitons and the inverse scattering transform. SIAM, Philadelphia, 1985

  2. Ablowitz, M.J., Ramani, A., Segur, H. A connection between nonlinear evolution equations and ordinary differential equations of p-type I. J. Math. Phys., 21:715–721 (1980)

    Article  MATH  Google Scholar 

  3. Cariello, F., Tabor, M. Similarity reductions from extended painlevé expansions for nonintegrable evolution equation. Physica D., 53:59–70 (1991)

    Article  MATH  Google Scholar 

  4. Hong, W.P., Jung, Y.D. Auto-baclund transformation and analytic solutions for general variable coefficient kdv equation. Phys. Lett. A., 257:149–152 (1999)

    Article  MATH  Google Scholar 

  5. Hong, W.P. Backlund transformation for a generalized burgers equation and solitonic solutions. Phys. Lett. A.,268:81–84 (2000)

    Article  MATH  Google Scholar 

  6. Hutlsman, W.D., Halford, M.V. Exact solutions to kdv equations with variable coefficients and/or nonuniformities. Comp. Math. Applic., 29(1):39–47 (1995)

    Google Scholar 

  7. Kawahara, T., Tanaka, M. Interactions of traveling fronts:an exact solution of a nonlinear diffusion equation. Physics Letters., 97A(8):311–314 (1983)

    Google Scholar 

  8. Nirmala, N., Vedan, M.J., Baby, B.V. Auto-baclund transformation, lax pairs, and painlevé property of a variable coefficient korteweg-de vries equation with nonuniformities. J. Math. Phys., 27(11):2640–2643 (1986)

    Article  MATH  Google Scholar 

  9. Steeb, W.H., Euler, N. Nonlinear evolution equations and painlevé test. World Scientific, Singapore, 1988

  10. Tian, B., Gao, Y.T. Truncated painlevé expansion and a wide-ranging type of generalized variable-coefficient kadomtsev-petviashvili equations. Phys. Lett. A., 209(5):297–304 (1995)

    Article  MATH  Google Scholar 

  11. Ŭgurlu, S. Y., Kart, C. The painlev é property and bäcklund transformation for fisher’s equation. Int. J. Comput. Numer. Anal. Appl., 3(3):297–303 (2003)

    Google Scholar 

  12. Weiss, J., Tabor, M., Carnevale, G. The painlevé property for partial differential equations. J. Math. Phys., 24(3):522–526 (1983)

    Article  MATH  Google Scholar 

  13. Weiss, J.J. The painlevé property for partial differential equations. II. Math. Phys., Bäcklund Transformation, Lax Pairs, and the Schwarzian Derivative. 24(6):1405–1413 (1983)

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Correspondence to Arzu Öğün.

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Öğün, A., Kart, C. Exact Solutions of Fisher and Generalized Fisher Equations with Variable Coefficients. Acta Mathematicae Applicatae Sinica, English Series 23, 563–568 (2007). https://doi.org/10.1007/s10255-007-0395

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  • DOI: https://doi.org/10.1007/s10255-007-0395

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