Research Article
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Year 2016, , 55 - 62, 15.04.2016
https://doi.org/10.36753/mathenot.421403

Abstract

References

  • [1] Ablowitz, M. J. and Clarkson, P. A., Solitons, Non-linear evolution equations and inverse scattering transform. Cambridge University Press, Cambridge, 1991.
  • [2] Malfliet, W., Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 (1992), no. 7, 650-654.
  • [3] Hirota R. and Satsuma, J., Soliton solutions of a coupled Korteweg-de Vries equation. Phys. Lett. A 85 (1981), 407-408.
  • [4] Wang, M. L., Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 213 (1996), 279-287.
  • [5] Wang, M., Solitary wave solutions for variant Boussinesq equations. Phys. Lett. A 199 (1995), 169-172.
  • [6] Zhang, S., Dong, L., Ba, J. M. and Sun, Y. N., The (G /G)-expansion method for discrete nonlinear Schrodinger equation. Pramana - J. Phys. 74 (2010), no. 2, 207-218.
  • [7] He, J. H. and Wu, X. H., Exp-function method for nonlinear wave equations. Chaos Soliton. Fract. 30 (2006), 700-708.
  • [8] Ma, W. X., Wu, H. Y. and He, J. S., Partial differential equations possessing Frobenius integrable decompositions. Phys. Lett. A 364 (2007), 29-32.
  • [9] Liu, C.S., Using trial equation method to solve the exact solutions for two kinds of KdV equations with variable coefficients. Acta Phys. Sin. 54 (2005), no. 10, 4506-4510.
  • [10] Liu, C.S., Trial equation method to nonlinear evolution equations with rank inhomogeneous: Mathematical discussions and its applications. Commun. Theor. Phys. 45 (2006), no. 2, 219-223.
  • [11] Liu, C.S., A new trial equation method and its applications. Commun. Theor. Phys. 45 (2006), no. 3, 395-397.
  • [12] Du, X.H., An irrational trial equation method and its applications. Pramana - J. Phys. 75 (2010), no. 3, 415-422.
  • [13] Liu, Y., Exact solutions to nonlinear Schrodinger equation with variable coefficients. Appl. Math. Comput. 217 (2011), 5866-5869.
  • [14] Gurefe, Y., Sonmezoglu, A. and Misirli, E., Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics. Pramana - J. Phys. 77 (2011), no. 6, 2013-2019.
  • [15] Odabasi, M. and Misirli, E., On the solutions of the nonlinear fractional differential equations via the modified trial equation method. Math. Method Appl. Sci. (2015), DOI: 10.1002/mma.3533.
  • [16] Odabasi, M. and Misirli, E., On the solutions of the nonlinear fractional differential equations via the modified trial equation method. Mathematical Sciences and Applications E-Notes 2 (2014), no. 1, 28-33.
  • [17] Yang, L., Hou, X.R. and Zeng, Z.B., A complete discrimination system for polynomials. Science in China (Series E) 39 (1996), no. 6, 628-646.
  • [18] Kutluay, S., Esen, A. and Tasbozan, O., The expansion method for some nonlinear evolution equations. Appl. Math. Comput. 217 (2010), no. 6, 384-391.
  • [19] Boyd, J.P., An analytical and numerical study of the two-dimensional Bratu equation. Journal of Scientific Computing 1 (1986), 183-206.
  • [20] Kabir, M.M., Analytic solutions for generalized forms of the nonlinear heat conduction equation. Journal of Scientific Computing 12 (2011), 2681-2691.
  • [21] Alagesan, T., Chung, Y. and Nakkeeran, K., Soliton solutions of coupled nonlinear Klein-Gordon equations. Chaos Soliton. Fract. 21 (2004), 879-882.
  • [22] Bulut, H. and Pandir, Y., Modified trial equation method to the nonlinear fractional Sharma-Tasso-Olever equation. International Journal of Modeling and Optimization 3 (2013), no. 4, 353-357.

Exact Traveling Wave Solutions of some Nonlinear Evolution Equations

Year 2016, , 55 - 62, 15.04.2016
https://doi.org/10.36753/mathenot.421403

Abstract

In nonlinear sciences, it is important to obtain traveling wave solutions of nonlinear evolution equations
to understand the phenomena they describe. In this study, we obtained the exact traveling wave solutions
of the Liouville equation, two-dimensional Bratu equation, generalized heat conduction equation and
coupled nonlinear Klein-Gordon equations by means of the trial equation method and the complete
discrimination system. This method is reliable, effective and enables to get soliton, single-kink and
compacton solutions of the generalized nonlinear evolution equations and systems of equations.

References

  • [1] Ablowitz, M. J. and Clarkson, P. A., Solitons, Non-linear evolution equations and inverse scattering transform. Cambridge University Press, Cambridge, 1991.
  • [2] Malfliet, W., Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 (1992), no. 7, 650-654.
  • [3] Hirota R. and Satsuma, J., Soliton solutions of a coupled Korteweg-de Vries equation. Phys. Lett. A 85 (1981), 407-408.
  • [4] Wang, M. L., Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 213 (1996), 279-287.
  • [5] Wang, M., Solitary wave solutions for variant Boussinesq equations. Phys. Lett. A 199 (1995), 169-172.
  • [6] Zhang, S., Dong, L., Ba, J. M. and Sun, Y. N., The (G /G)-expansion method for discrete nonlinear Schrodinger equation. Pramana - J. Phys. 74 (2010), no. 2, 207-218.
  • [7] He, J. H. and Wu, X. H., Exp-function method for nonlinear wave equations. Chaos Soliton. Fract. 30 (2006), 700-708.
  • [8] Ma, W. X., Wu, H. Y. and He, J. S., Partial differential equations possessing Frobenius integrable decompositions. Phys. Lett. A 364 (2007), 29-32.
  • [9] Liu, C.S., Using trial equation method to solve the exact solutions for two kinds of KdV equations with variable coefficients. Acta Phys. Sin. 54 (2005), no. 10, 4506-4510.
  • [10] Liu, C.S., Trial equation method to nonlinear evolution equations with rank inhomogeneous: Mathematical discussions and its applications. Commun. Theor. Phys. 45 (2006), no. 2, 219-223.
  • [11] Liu, C.S., A new trial equation method and its applications. Commun. Theor. Phys. 45 (2006), no. 3, 395-397.
  • [12] Du, X.H., An irrational trial equation method and its applications. Pramana - J. Phys. 75 (2010), no. 3, 415-422.
  • [13] Liu, Y., Exact solutions to nonlinear Schrodinger equation with variable coefficients. Appl. Math. Comput. 217 (2011), 5866-5869.
  • [14] Gurefe, Y., Sonmezoglu, A. and Misirli, E., Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics. Pramana - J. Phys. 77 (2011), no. 6, 2013-2019.
  • [15] Odabasi, M. and Misirli, E., On the solutions of the nonlinear fractional differential equations via the modified trial equation method. Math. Method Appl. Sci. (2015), DOI: 10.1002/mma.3533.
  • [16] Odabasi, M. and Misirli, E., On the solutions of the nonlinear fractional differential equations via the modified trial equation method. Mathematical Sciences and Applications E-Notes 2 (2014), no. 1, 28-33.
  • [17] Yang, L., Hou, X.R. and Zeng, Z.B., A complete discrimination system for polynomials. Science in China (Series E) 39 (1996), no. 6, 628-646.
  • [18] Kutluay, S., Esen, A. and Tasbozan, O., The expansion method for some nonlinear evolution equations. Appl. Math. Comput. 217 (2010), no. 6, 384-391.
  • [19] Boyd, J.P., An analytical and numerical study of the two-dimensional Bratu equation. Journal of Scientific Computing 1 (1986), 183-206.
  • [20] Kabir, M.M., Analytic solutions for generalized forms of the nonlinear heat conduction equation. Journal of Scientific Computing 12 (2011), 2681-2691.
  • [21] Alagesan, T., Chung, Y. and Nakkeeran, K., Soliton solutions of coupled nonlinear Klein-Gordon equations. Chaos Soliton. Fract. 21 (2004), 879-882.
  • [22] Bulut, H. and Pandir, Y., Modified trial equation method to the nonlinear fractional Sharma-Tasso-Olever equation. International Journal of Modeling and Optimization 3 (2013), no. 4, 353-357.
There are 22 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Meryem Odabasi

Emine Misirli

Publication Date April 15, 2016
Submission Date September 12, 2015
Published in Issue Year 2016

Cite

APA Odabasi, M., & Misirli, E. (2016). Exact Traveling Wave Solutions of some Nonlinear Evolution Equations. Mathematical Sciences and Applications E-Notes, 4(1), 55-62. https://doi.org/10.36753/mathenot.421403
AMA Odabasi M, Misirli E. Exact Traveling Wave Solutions of some Nonlinear Evolution Equations. Math. Sci. Appl. E-Notes. April 2016;4(1):55-62. doi:10.36753/mathenot.421403
Chicago Odabasi, Meryem, and Emine Misirli. “Exact Traveling Wave Solutions of Some Nonlinear Evolution Equations”. Mathematical Sciences and Applications E-Notes 4, no. 1 (April 2016): 55-62. https://doi.org/10.36753/mathenot.421403.
EndNote Odabasi M, Misirli E (April 1, 2016) Exact Traveling Wave Solutions of some Nonlinear Evolution Equations. Mathematical Sciences and Applications E-Notes 4 1 55–62.
IEEE M. Odabasi and E. Misirli, “Exact Traveling Wave Solutions of some Nonlinear Evolution Equations”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 55–62, 2016, doi: 10.36753/mathenot.421403.
ISNAD Odabasi, Meryem - Misirli, Emine. “Exact Traveling Wave Solutions of Some Nonlinear Evolution Equations”. Mathematical Sciences and Applications E-Notes 4/1 (April 2016), 55-62. https://doi.org/10.36753/mathenot.421403.
JAMA Odabasi M, Misirli E. Exact Traveling Wave Solutions of some Nonlinear Evolution Equations. Math. Sci. Appl. E-Notes. 2016;4:55–62.
MLA Odabasi, Meryem and Emine Misirli. “Exact Traveling Wave Solutions of Some Nonlinear Evolution Equations”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, 2016, pp. 55-62, doi:10.36753/mathenot.421403.
Vancouver Odabasi M, Misirli E. Exact Traveling Wave Solutions of some Nonlinear Evolution Equations. Math. Sci. Appl. E-Notes. 2016;4(1):55-62.

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