Document Type: Research Paper

Authors

1 Department of Mathematics, Islamic Azad University, Firuozkooh branch, Firuozkooh, IRAN

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, 14778, Iran

Abstract

In this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. We transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters Value, Ambiguity and Fuzziness. 

Keywords

[1]          Wazwaz A.M., The tanh method: Exact solutions of the Sine–Gordon and Sinh– Gordon equations, Appl. Math. Comput. 167, 1196–1210, 2005.

[2]          Mal.iet W., Hereman W. The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Phys Scr, 54(56), 3–8, 1996.                   

[3]          Wazwaz A.M., The tanh and the sine–cosine methods for a reliable treatment of the modified equal width equation and its variants.Commun Nonlinear Sci Numer Simu, 11(1), 48–60, 2006.

[4]          Biazar J.,Ghazvini H., Exact solutions for non-linear Schrödinger equations by He’s homotopy perturbation method Physics Letters A, 366, 79-84, 2007.

[5]          He J.H., Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals, 26, 695–700, 2005.

[6]          He J.H., Variational iteration method—a kind of non-linear analytical technique: some examples, Int. J. Nonlinear Mech, 34, 699–708, 1999.

[7]          He J.H., Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput, 114, 115–123, 2000

[8]          Biazar J., Babolian E., Nouri A., Islam R., An alternate algorithm for computing Adomian Decomposition method in special cases, Applied Mathematics and Computation, 38 (2-3), 523- 529, 2003.

[9]          He J.H., Wu X.H., Exp-function method for nonlinear wave equations, Chaos Solitons Fractals 30, 700–708, 2006.

[10]      Zhang S., Application of Exp-function method to a KdV equation with variable coefficients, Phys. Lett. A 365, 448–453, 2007.

[11]      biazar J., ayati z., Application of Exp-function method to Equal-width wave equation, Physica Scripta ,78, 045005, 2008.

[12]      Wang M.L., Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A 213, 279, 1996.

[13]      Abdou M.A., The extended F-expansion method and its application for a class of nonlinear evolution equations, Chaos Solitons Fractals, 31, 95-104, 2007.

[14]      Wang M.L., Li X.Z., Zhang J.L., The expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, phys. Lett. A 372, 417–423, 2008.

[15]      Zhang S.A., generalized _ expansion method for the mKdV equation with variable coef.cients. Phys Lett A  372(13),2254–7, 2008.

[16]      Boiti M., Leon J.J.P., Pempinelli F., Spectral transform for a two spatial dimension extension of the dispersive long wave equation, Inverse Probl. 3, 371–387, 1987.

[17]      Paquin G., and Winternitz P., Group theoretical analysis of dispersive long wave equations equation in two space dimensions, Physica D, 46,122-138, 1990.

[18]      Lou S.Y., Nonclassical symmetry reductions for the dispersive wave equations in shallow water. J Math Phys, 33,4300–5, 1992.

[19]      Lou S.Y., Similarity solutions of dispersive long wave equations in two space dimensions, Math. Meth. Appl. Sci, ,18, 789-802, 1995.

[20]      Lou S. Y., Symmetries and algebras of the integrable dispersive long wave equations in (2+1)- dimensional spaces, J. Phys. A, 27, 3235-3243, 1994.

[21]      Zhang J. F., BBlund transformation and multisoliton-like solution of the (2+1)-dimensional dispersive long wave equations, Commun. Theor. Phys., 33, 577-582, 2000.

[22]      Kong C., Wang D., Song L., Zhang H., New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method, Chaos Solitons and Fractals xxx,xxx–xxx, 2007.