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Exact solutions of the Zakharov equations by using the first integral method

Year 2012, Volume: 61 Issue: 2, 9 - 16, 01.08.2012
https://doi.org/10.1501/Commua1_0000000676

Abstract

In this paper some traveling wave solutions of the Zakharov equations are obtained by using the first integral method. The first integral method
is a powerful an effective method for solving nonlinear partial differential equations

References

  • Abbasbandy, S., Shirzadi, A., The …rst integral method for modi…ed Benjamin-Bona-Mahony equation, Commun. Nonlinear Sci. Numer. Simul. 15 (2010) no. 7 1759–1764
  • Ablowitz, M., Segur, H., Solitons and the inverse scattering transform. SIAM, Philadelphia, Ali,A. H. A., Raslan, K. R., The …rst integral method for solving a system of nonlinear partial diğ erential equations, Int. J. Nonlinear Sci. 5 (2008) no. 2 111–119
  • Deng, X., Exact peaked wave solution of CH- Math. Comput. 206 (2008) no. 2 806–809 equation by the …rst-integral method, Appl.
  • Ding T. R., Li C. Z., Ordinary diğerential equations. Peking: Peking University Press; 1996
  • Feng, Z.S., The …rst-integral method to the Burgers–KdV equation, J. Phys. A 35 (2002) –350
  • Feng, Z.S., Wang, X.H., The …rst integral method to the two-dimensional Burgers-KdV equa- tion, Phys. Lett. A 308 (2003) 173 - 178
  • Gao, Yi-Tian, B. Tian, Generalized tanh method with symbolic computation and generalized shallow water wave equation, Comput. Math. Appl. 33 (1997) no. 4, 115–118
  • Hirota R. Direct method of …nding exact solutions of nonlinear evolution equations, In: Bullough R, Caudrey P, editors. Backlund transformations. Berlin, Springer, 1980. p. 1157
  • Hong, W. P., Jung, Y. D., Auto-bäclund transformation and analytic solutions for general variable coe¢ cient KdV equation, Phys. Lett. A 257 (1999) 149–152
  • Ke, Yun-Quan; Yu, Jun, The …rst integral method to study a class of reaction-diğ usion equations, Commun. Theor. Phys. (Beijing) 43 (2005) no. 4 597–600
  • Khater, A. H., Mal*iet, W., Callebaut D. K. and Kamel, E.S., The tanh method, a sim- ple transformation and exact analytical solutions for nonlinear reactiondiğ usion equations, Chaos Solitons Fractals 14(3) (2002) 513 - 522
  • Li, B., Chen, Y., Zhang, H., Bäcklund transformation and exact solutions for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order. Phys. Lett. A 305 (2002) 377-382
  • Lu, B., Zhang, H.Q., Xie F.D., Travelling wave solutions of nonlinear partial equations by using the …rst integral method, Appl. Math. Comput. 216 (2010) no. 4 1329–1336
  • Melrose, D. B., The Zakharov Equations: a derivation using kinetic theory, J. Plasma Phys. (1987) 241-246
  • Ö¼gün, A.,Kart, C., Exact solutions of Fisher and generalized Fisher equations with variable coe¢ cients, Acta Math. Appl. Sin. Engl Ser. 23 (2007) no. 4, 563-568
  • Raslan, K. R., The …rst integral method for solving some important nonlinear partial diğ er- ential equations, Nonlinear Dynam. 53 (2008) no. 4 281–286
  • Taghizadeh, N., Mirzazadeh, M., Farahrooz, F., Exact solutions of the nonlinear Schrödinger equation by the …rst integral method, J. Math. Anal. Appl. 374 (2011) no. 2 549–553
  • Ta¸scan, F., Bekir, A., Travelling wave solutions of the Cahn-Allen equation by using …rst integral method, Appl. Math. Comput. 207 (2009) no. 1 279–282
  • Vakhnenko, V. O., Parkes, E. J., Morrison, A. J., A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos Soliton Fractals (4) (2003) 683-692
  • Weiss, J., Tabor, M., Carnevale, G., The Painlevé property for partial diğ erential equations, J. Math. Phys. 24 (3) (1983) 522-526
  • Zwillinger, D., Handbook of diğerential equations, Academic Press, London, 1998
  • Current address : Arzu Ünal, Department of Mathematics, Faculty of Science, Ankara Univer- sity, 06100 Ankara, TURKEY
Year 2012, Volume: 61 Issue: 2, 9 - 16, 01.08.2012
https://doi.org/10.1501/Commua1_0000000676

Abstract

References

  • Abbasbandy, S., Shirzadi, A., The …rst integral method for modi…ed Benjamin-Bona-Mahony equation, Commun. Nonlinear Sci. Numer. Simul. 15 (2010) no. 7 1759–1764
  • Ablowitz, M., Segur, H., Solitons and the inverse scattering transform. SIAM, Philadelphia, Ali,A. H. A., Raslan, K. R., The …rst integral method for solving a system of nonlinear partial diğ erential equations, Int. J. Nonlinear Sci. 5 (2008) no. 2 111–119
  • Deng, X., Exact peaked wave solution of CH- Math. Comput. 206 (2008) no. 2 806–809 equation by the …rst-integral method, Appl.
  • Ding T. R., Li C. Z., Ordinary diğerential equations. Peking: Peking University Press; 1996
  • Feng, Z.S., The …rst-integral method to the Burgers–KdV equation, J. Phys. A 35 (2002) –350
  • Feng, Z.S., Wang, X.H., The …rst integral method to the two-dimensional Burgers-KdV equa- tion, Phys. Lett. A 308 (2003) 173 - 178
  • Gao, Yi-Tian, B. Tian, Generalized tanh method with symbolic computation and generalized shallow water wave equation, Comput. Math. Appl. 33 (1997) no. 4, 115–118
  • Hirota R. Direct method of …nding exact solutions of nonlinear evolution equations, In: Bullough R, Caudrey P, editors. Backlund transformations. Berlin, Springer, 1980. p. 1157
  • Hong, W. P., Jung, Y. D., Auto-bäclund transformation and analytic solutions for general variable coe¢ cient KdV equation, Phys. Lett. A 257 (1999) 149–152
  • Ke, Yun-Quan; Yu, Jun, The …rst integral method to study a class of reaction-diğ usion equations, Commun. Theor. Phys. (Beijing) 43 (2005) no. 4 597–600
  • Khater, A. H., Mal*iet, W., Callebaut D. K. and Kamel, E.S., The tanh method, a sim- ple transformation and exact analytical solutions for nonlinear reactiondiğ usion equations, Chaos Solitons Fractals 14(3) (2002) 513 - 522
  • Li, B., Chen, Y., Zhang, H., Bäcklund transformation and exact solutions for compound KdV-type and compound KdV–Burgers-type equations with nonlinear terms of any order. Phys. Lett. A 305 (2002) 377-382
  • Lu, B., Zhang, H.Q., Xie F.D., Travelling wave solutions of nonlinear partial equations by using the …rst integral method, Appl. Math. Comput. 216 (2010) no. 4 1329–1336
  • Melrose, D. B., The Zakharov Equations: a derivation using kinetic theory, J. Plasma Phys. (1987) 241-246
  • Ö¼gün, A.,Kart, C., Exact solutions of Fisher and generalized Fisher equations with variable coe¢ cients, Acta Math. Appl. Sin. Engl Ser. 23 (2007) no. 4, 563-568
  • Raslan, K. R., The …rst integral method for solving some important nonlinear partial diğ er- ential equations, Nonlinear Dynam. 53 (2008) no. 4 281–286
  • Taghizadeh, N., Mirzazadeh, M., Farahrooz, F., Exact solutions of the nonlinear Schrödinger equation by the …rst integral method, J. Math. Anal. Appl. 374 (2011) no. 2 549–553
  • Ta¸scan, F., Bekir, A., Travelling wave solutions of the Cahn-Allen equation by using …rst integral method, Appl. Math. Comput. 207 (2009) no. 1 279–282
  • Vakhnenko, V. O., Parkes, E. J., Morrison, A. J., A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos Soliton Fractals (4) (2003) 683-692
  • Weiss, J., Tabor, M., Carnevale, G., The Painlevé property for partial diğ erential equations, J. Math. Phys. 24 (3) (1983) 522-526
  • Zwillinger, D., Handbook of diğerential equations, Academic Press, London, 1998
  • Current address : Arzu Ünal, Department of Mathematics, Faculty of Science, Ankara Univer- sity, 06100 Ankara, TURKEY
There are 22 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Arzu Öğün Ünal This is me

Publication Date August 1, 2012
Published in Issue Year 2012 Volume: 61 Issue: 2

Cite

APA Öğün Ünal, A. (2012). Exact solutions of the Zakharov equations by using the first integral method. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 61(2), 9-16. https://doi.org/10.1501/Commua1_0000000676
AMA Öğün Ünal A. Exact solutions of the Zakharov equations by using the first integral method. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2012;61(2):9-16. doi:10.1501/Commua1_0000000676
Chicago Öğün Ünal, Arzu. “Exact Solutions of the Zakharov Equations by Using the First Integral Method”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 61, no. 2 (August 2012): 9-16. https://doi.org/10.1501/Commua1_0000000676.
EndNote Öğün Ünal A (August 1, 2012) Exact solutions of the Zakharov equations by using the first integral method. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 61 2 9–16.
IEEE A. Öğün Ünal, “Exact solutions of the Zakharov equations by using the first integral method”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 61, no. 2, pp. 9–16, 2012, doi: 10.1501/Commua1_0000000676.
ISNAD Öğün Ünal, Arzu. “Exact Solutions of the Zakharov Equations by Using the First Integral Method”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 61/2 (August 2012), 9-16. https://doi.org/10.1501/Commua1_0000000676.
JAMA Öğün Ünal A. Exact solutions of the Zakharov equations by using the first integral method. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2012;61:9–16.
MLA Öğün Ünal, Arzu. “Exact Solutions of the Zakharov Equations by Using the First Integral Method”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 61, no. 2, 2012, pp. 9-16, doi:10.1501/Commua1_0000000676.
Vancouver Öğün Ünal A. Exact solutions of the Zakharov equations by using the first integral method. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2012;61(2):9-16.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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