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Year 2012, Volume: 4 Issue: 2, 26 - 34, 01.06.2012

Abstract

References

  • Debtnath,L., Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhauser, Boston, MA, 1997.
  • Wazwaz,A.M. Partial Differential Equations: Methods and Applications, Balkema, Rotterdam, 2002.
  • Hereman,W.,Banerjee,P.P.,Korpel,A.,Assanto,G.,van Immerzeele, A. andMeerpoel,A., Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method, J. Phys. A: Math. Gen. 19,607-628, 1986.
  • Khater,A.H.,Helal,M.A.,El-Kalaawy,O.H., Backlund transformations: exact solutions for the KdV and the Calogero - Degasperis-FokasmKdV equations, Math. Methods Appl. Sci. ,719-731,1998.
  • Wazwaz,A.M., A study of nonlinear dispersive equations with solitary-wave solutions having compact support, Math. Comput.Simulation 56,269-276, 2001.
  • Elwakil,S.A.,El-Labany, S.K.,Zahran,M.A.,Sabry,R., Modified extended tanh-function method for solving nonlinear partial differential equations, Phys. Lett. A 299,179-188,2002.
  • Lei,Y.,Fajiang,Z.,Yinghai,W., The homogeneous balance method, Lax pair, Hirota transformation and a generalfifth-orderKdVequation, Chaos, Solitons& Fractals 13 337- ,2002.
  • Zhang,J.F., New exactsolitarywavesolutionsofthe KS equation, Int. J. Theor. Phys., ,1829-1834,1999.
  • Wang,M.L., Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A ,279-287,1996.
  • Wang,M.L.,Zhou, Y.B., andLi, Z.B., Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Phys. Lett. A 216,67-75,1996.
  • Malfliet,M.L., Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60 654,1992.
  • Parkes,E.J.andDuffy,B.R., An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Comput. Phys. Commun, 98, 288-300,1996.
  • Duffy,B.R., andParkes,E.J., Travelling solitary wave solutions to a seventh-order generalized KdV equation, Phys. Lett. A 214,271-272,1996.
  • Parkes,E.J., andDuffy,B.R., Travelling solitary wave solutions to a compound KdV- Burgers equation, Phys. Lett. A 229,217-220,1997.
  • Inan,I. E., Exact solutions for coupled KdV equation and KdV equations, Phys. Lett. A ,90-95,2007.
  • Fan,E.G., Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277,212-218,2000.
  • Perring, J. K., andSkyrme,T. H.,A model unified field equation,Nucl.Phys.31,550– ,1962.
  • Ablowitz,M. J.,Herbst,B. M., andSchober,C.,On the numerical solution of the Sine– Gordon equation. J.Comput.Phys.126,299–314,1996.
  • Wazwaz,A.M., The tanh method: solitons and periodic solutions for the Dodd– Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations, Chaos, Solitons& Fractals ,55-63,2005.
  • Wazwaz,A. M., The variable separated ODE method for a reliable treatment for the Liouville equation and its variants, Commun. Nonlinear Sci. 12,434–446,2007.
  • Borhanifar,A., andMoghanlu, A. Z., Application of the expansion method for the Zhiber–Shabat equation and other related equations, Math. Comput.Model.54,2109– ,2011.
  • Fan,E., andHon,Y. C., Applications of extended tanh method to special types of nonlinear equations, Appl. Math. Comput.141,351–358,2003.
  • He, J. H., and Wu,X. H.,Exp-function method for nonlinear wave equations, Chaos, Solitons and Fractals 30,700–708,2006.
  • Zhang,H., New Exact Travelling wave solutions of the generalized Zakharov equations, Rep. Math. Phys. 60,97-106,2007.

VARIOUS EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS BY A DIRECT ALGEBRAIC METHOD

Year 2012, Volume: 4 Issue: 2, 26 - 34, 01.06.2012

Abstract

In this paper, we implemented a direct algebraic method for the exact solutions of the Liouville equation, DoddBullough-Mikhailov equations. By using this method, we find several exact solutions of the Liouville equation, Dodd-Bullough-Mikhailov equations

References

  • Debtnath,L., Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhauser, Boston, MA, 1997.
  • Wazwaz,A.M. Partial Differential Equations: Methods and Applications, Balkema, Rotterdam, 2002.
  • Hereman,W.,Banerjee,P.P.,Korpel,A.,Assanto,G.,van Immerzeele, A. andMeerpoel,A., Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method, J. Phys. A: Math. Gen. 19,607-628, 1986.
  • Khater,A.H.,Helal,M.A.,El-Kalaawy,O.H., Backlund transformations: exact solutions for the KdV and the Calogero - Degasperis-FokasmKdV equations, Math. Methods Appl. Sci. ,719-731,1998.
  • Wazwaz,A.M., A study of nonlinear dispersive equations with solitary-wave solutions having compact support, Math. Comput.Simulation 56,269-276, 2001.
  • Elwakil,S.A.,El-Labany, S.K.,Zahran,M.A.,Sabry,R., Modified extended tanh-function method for solving nonlinear partial differential equations, Phys. Lett. A 299,179-188,2002.
  • Lei,Y.,Fajiang,Z.,Yinghai,W., The homogeneous balance method, Lax pair, Hirota transformation and a generalfifth-orderKdVequation, Chaos, Solitons& Fractals 13 337- ,2002.
  • Zhang,J.F., New exactsolitarywavesolutionsofthe KS equation, Int. J. Theor. Phys., ,1829-1834,1999.
  • Wang,M.L., Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A ,279-287,1996.
  • Wang,M.L.,Zhou, Y.B., andLi, Z.B., Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Phys. Lett. A 216,67-75,1996.
  • Malfliet,M.L., Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60 654,1992.
  • Parkes,E.J.andDuffy,B.R., An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Comput. Phys. Commun, 98, 288-300,1996.
  • Duffy,B.R., andParkes,E.J., Travelling solitary wave solutions to a seventh-order generalized KdV equation, Phys. Lett. A 214,271-272,1996.
  • Parkes,E.J., andDuffy,B.R., Travelling solitary wave solutions to a compound KdV- Burgers equation, Phys. Lett. A 229,217-220,1997.
  • Inan,I. E., Exact solutions for coupled KdV equation and KdV equations, Phys. Lett. A ,90-95,2007.
  • Fan,E.G., Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277,212-218,2000.
  • Perring, J. K., andSkyrme,T. H.,A model unified field equation,Nucl.Phys.31,550– ,1962.
  • Ablowitz,M. J.,Herbst,B. M., andSchober,C.,On the numerical solution of the Sine– Gordon equation. J.Comput.Phys.126,299–314,1996.
  • Wazwaz,A.M., The tanh method: solitons and periodic solutions for the Dodd– Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations, Chaos, Solitons& Fractals ,55-63,2005.
  • Wazwaz,A. M., The variable separated ODE method for a reliable treatment for the Liouville equation and its variants, Commun. Nonlinear Sci. 12,434–446,2007.
  • Borhanifar,A., andMoghanlu, A. Z., Application of the expansion method for the Zhiber–Shabat equation and other related equations, Math. Comput.Model.54,2109– ,2011.
  • Fan,E., andHon,Y. C., Applications of extended tanh method to special types of nonlinear equations, Appl. Math. Comput.141,351–358,2003.
  • He, J. H., and Wu,X. H.,Exp-function method for nonlinear wave equations, Chaos, Solitons and Fractals 30,700–708,2006.
  • Zhang,H., New Exact Travelling wave solutions of the generalized Zakharov equations, Rep. Math. Phys. 60,97-106,2007.
There are 24 citations in total.

Details

Other ID JA66AH87UT
Journal Section Articles
Authors

Y. Ugurlu This is me

I.E. Inan This is me

Publication Date June 1, 2012
Published in Issue Year 2012 Volume: 4 Issue: 2

Cite

APA Ugurlu, Y., & Inan, I. (2012). VARIOUS EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS BY A DIRECT ALGEBRAIC METHOD. International Journal of Engineering and Applied Sciences, 4(2), 26-34.
AMA Ugurlu Y, Inan I. VARIOUS EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS BY A DIRECT ALGEBRAIC METHOD. IJEAS. June 2012;4(2):26-34.
Chicago Ugurlu, Y., and I.E. Inan. “VARIOUS EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS BY A DIRECT ALGEBRAIC METHOD”. International Journal of Engineering and Applied Sciences 4, no. 2 (June 2012): 26-34.
EndNote Ugurlu Y, Inan I (June 1, 2012) VARIOUS EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS BY A DIRECT ALGEBRAIC METHOD. International Journal of Engineering and Applied Sciences 4 2 26–34.
IEEE Y. Ugurlu and I. Inan, “VARIOUS EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS BY A DIRECT ALGEBRAIC METHOD”, IJEAS, vol. 4, no. 2, pp. 26–34, 2012.
ISNAD Ugurlu, Y. - Inan, I.E. “VARIOUS EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS BY A DIRECT ALGEBRAIC METHOD”. International Journal of Engineering and Applied Sciences 4/2 (June 2012), 26-34.
JAMA Ugurlu Y, Inan I. VARIOUS EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS BY A DIRECT ALGEBRAIC METHOD. IJEAS. 2012;4:26–34.
MLA Ugurlu, Y. and I.E. Inan. “VARIOUS EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS BY A DIRECT ALGEBRAIC METHOD”. International Journal of Engineering and Applied Sciences, vol. 4, no. 2, 2012, pp. 26-34.
Vancouver Ugurlu Y, Inan I. VARIOUS EXACT SOLUTIONS OF SOME NONLINEAR EQUATIONS BY A DIRECT ALGEBRAIC METHOD. IJEAS. 2012;4(2):26-34.

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