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Genişletilmiş Dönüştürülmüş Rasyonel Fonksiyon Metodunun Bazı 3+1 Boyutlu Lineer Olmayan Oluşum Denklemlerine Uygulanması

Year 2018, Volume: 8 Issue: 2, 433 - 437, 01.06.2018

Abstract

Dönüştürülmüş rasyonel fonksiyon metodu; tanh tipi metodlar, homojen denge metodu, resmetme metodu, üstel fonksiyon metodu ve F-açılım tipi metodların birleşimi olarak düşünülebilir. Biz bu çalışmada, lineer olmayan oluşum denklemlerinin kompleksiton çözümlerinin elde edilmesinde kullanışlı ve etkili bir yol olan genişletilmiş dönüştürülmüş rasyonel fonksiyon metodunu kullanarak 3+1 boyutlu KdV ve yeni 3+1 boyutlu genelleştirilmiş Kadomtsev-Petviashvili denklemlerinin kompleksiton çözümlerini elde edeceğiz

References

  • Matveev, VB., Salle, MA. 1980. Darboux transformation and solutions. Springer, Berlin.
  • Wang, ML. 1995. Solitary wave solutions for variant Boussinesq equations. Phys. Lett. A, 199: 169-172.
  • Zhou, Y., Wang, ML., Wang, YM., 2003. Periodic wave solutions to a coupled KdV equations with variable coefficients. Phys. Lett. A, 308: 31-36.
  • Parkes, EJ., Duffy BR. 1996. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Comput. Phys. Commun., 98: 288-300.
  • Ma, WX. 1993. Travelling wave solutions to a seventh order generalized KdV equation. Phys. Lett. A, 180: 221-224.
  • Fuchssteiner, B., Carillo, S. 1992. A new class of nonlinear partial differential equations solvable by quadratures. in: B. Fuchssteiner, W.A.J. Luxemburg (Eds.). Analysis and Geometry, BJ Wissenschaftsverlag, Mannheim; pp. 73-85.
  • Ma, WX., Fuchssteiner, B. 1996. Explicit and exact solutions to a Kolmogorov-Petrovshii-Piskunov equation. Int. J. Nonlinear Mech., 31: 329-338.
  • Fan, EG. 2000. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A, 77: 212-218.
  • Wazwaz, AM. 2006. New solitary wave solutions to the Kuramoto-Sivashinsky and the Kawahara equations. Appl. Math. Comput., 182: 1642-1650.
  • Wazwaz, AM. 2007. The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations. Appl. Math. Comput., 188: 1467-1475.
  • Lü, X., Chen, ST., Ma, WX. 2016. Constructing lump solutions to a generalized Kadomtsev-Petviashvili-Boussinesq equation. Nonlinear Dynam., 86: 523-534.
  • Lü, X., Ma, WX. 2016. Study of lump Dynamics based on a dimensionally reduced Hirota bilinear equation. Nonlinear Dynam., 85: 1217-1222.
  • Gao, LN., Zhao, XY., Zi, YY., Yu, J., Lü, X. 2016. Resonant behavior of multiple wave solutions to a Hirota bilinear equation. Comput. Math. Appl., 72: 1225-1229.
  • Lü, X., Ma, WX., Zhou, Y., Khalique, CM. 2016. Rational solutions to an extended Kadomtsev-Petviashvili-like equation with symbolic computation. Comput. Math. Appl., 71: 1560- 1567.
  • Lü, X., Ma, WX., Chen, ST., Khalique, CM. 2016. A note on rational solutions to a Hirota-Satsuma-like equation. Appl. Math. Lett., 58: 13-18.
  • Lü, X., Ma, WX., Yu, J., Khalique, CM. 2016. Solitary waves with the Madelung fluid description: A generalized derivative nonlinear Schrödinger equation. Commun. Nonlinear Sci., 31: 40-46.
  • Ma, WX. 2002. Complexiton solutions to the Kortweg-de Vries equation. Phys. Lett. A, 301: 35-44.
  • Ma, WX. 2005. Complexiton solutions to integrable equations. Nonlinear Anal., 63: e2461-e2471.
  • Wazwaz, AM., El-Tantawy, SA. 2016. A new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation. Nonlinear Dynam., 84: 1107-1112.
  • Yang, XD., Ruan, HY. 2013. HBFGen: A maple package to construct the Hirota bilinear form for nonlinear equations. Appl. Math. Comput., 219: 8018-8025.

Application of Extended Transformed Rational Function Method to Some 3+1 Dimensional Nonlinear Evolution Equations

Year 2018, Volume: 8 Issue: 2, 433 - 437, 01.06.2018

Abstract

The transformed rational function method can be considered as unification of the tanh type methods, the homogeneous balance method, the mapping method, the exp-function method and the F-expansion type methods. In this paper, we present complexiton solutions of 3+1 dimensional Korteweg-de Vries KdV equation and a new 3+1 dimensional generalized Kadomtsev-Petviashvili equation by using extended transformed rational function method which provides very useful and effective way to obtain complexiton solutions of nonlinear evolution equations.

References

  • Matveev, VB., Salle, MA. 1980. Darboux transformation and solutions. Springer, Berlin.
  • Wang, ML. 1995. Solitary wave solutions for variant Boussinesq equations. Phys. Lett. A, 199: 169-172.
  • Zhou, Y., Wang, ML., Wang, YM., 2003. Periodic wave solutions to a coupled KdV equations with variable coefficients. Phys. Lett. A, 308: 31-36.
  • Parkes, EJ., Duffy BR. 1996. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Comput. Phys. Commun., 98: 288-300.
  • Ma, WX. 1993. Travelling wave solutions to a seventh order generalized KdV equation. Phys. Lett. A, 180: 221-224.
  • Fuchssteiner, B., Carillo, S. 1992. A new class of nonlinear partial differential equations solvable by quadratures. in: B. Fuchssteiner, W.A.J. Luxemburg (Eds.). Analysis and Geometry, BJ Wissenschaftsverlag, Mannheim; pp. 73-85.
  • Ma, WX., Fuchssteiner, B. 1996. Explicit and exact solutions to a Kolmogorov-Petrovshii-Piskunov equation. Int. J. Nonlinear Mech., 31: 329-338.
  • Fan, EG. 2000. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A, 77: 212-218.
  • Wazwaz, AM. 2006. New solitary wave solutions to the Kuramoto-Sivashinsky and the Kawahara equations. Appl. Math. Comput., 182: 1642-1650.
  • Wazwaz, AM. 2007. The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations. Appl. Math. Comput., 188: 1467-1475.
  • Lü, X., Chen, ST., Ma, WX. 2016. Constructing lump solutions to a generalized Kadomtsev-Petviashvili-Boussinesq equation. Nonlinear Dynam., 86: 523-534.
  • Lü, X., Ma, WX. 2016. Study of lump Dynamics based on a dimensionally reduced Hirota bilinear equation. Nonlinear Dynam., 85: 1217-1222.
  • Gao, LN., Zhao, XY., Zi, YY., Yu, J., Lü, X. 2016. Resonant behavior of multiple wave solutions to a Hirota bilinear equation. Comput. Math. Appl., 72: 1225-1229.
  • Lü, X., Ma, WX., Zhou, Y., Khalique, CM. 2016. Rational solutions to an extended Kadomtsev-Petviashvili-like equation with symbolic computation. Comput. Math. Appl., 71: 1560- 1567.
  • Lü, X., Ma, WX., Chen, ST., Khalique, CM. 2016. A note on rational solutions to a Hirota-Satsuma-like equation. Appl. Math. Lett., 58: 13-18.
  • Lü, X., Ma, WX., Yu, J., Khalique, CM. 2016. Solitary waves with the Madelung fluid description: A generalized derivative nonlinear Schrödinger equation. Commun. Nonlinear Sci., 31: 40-46.
  • Ma, WX. 2002. Complexiton solutions to the Kortweg-de Vries equation. Phys. Lett. A, 301: 35-44.
  • Ma, WX. 2005. Complexiton solutions to integrable equations. Nonlinear Anal., 63: e2461-e2471.
  • Wazwaz, AM., El-Tantawy, SA. 2016. A new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation. Nonlinear Dynam., 84: 1107-1112.
  • Yang, XD., Ruan, HY. 2013. HBFGen: A maple package to construct the Hirota bilinear form for nonlinear equations. Appl. Math. Comput., 219: 8018-8025.
There are 20 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Ömer Ünsal This is me

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 2

Cite

APA Ünsal, Ö. (2018). Genişletilmiş Dönüştürülmüş Rasyonel Fonksiyon Metodunun Bazı 3+1 Boyutlu Lineer Olmayan Oluşum Denklemlerine Uygulanması. Karaelmas Fen Ve Mühendislik Dergisi, 8(2), 433-437.
AMA Ünsal Ö. Genişletilmiş Dönüştürülmüş Rasyonel Fonksiyon Metodunun Bazı 3+1 Boyutlu Lineer Olmayan Oluşum Denklemlerine Uygulanması. Karaelmas Fen ve Mühendislik Dergisi. June 2018;8(2):433-437.
Chicago Ünsal, Ömer. “Genişletilmiş Dönüştürülmüş Rasyonel Fonksiyon Metodunun Bazı 3+1 Boyutlu Lineer Olmayan Oluşum Denklemlerine Uygulanması”. Karaelmas Fen Ve Mühendislik Dergisi 8, no. 2 (June 2018): 433-37.
EndNote Ünsal Ö (June 1, 2018) Genişletilmiş Dönüştürülmüş Rasyonel Fonksiyon Metodunun Bazı 3+1 Boyutlu Lineer Olmayan Oluşum Denklemlerine Uygulanması. Karaelmas Fen ve Mühendislik Dergisi 8 2 433–437.
IEEE Ö. Ünsal, “Genişletilmiş Dönüştürülmüş Rasyonel Fonksiyon Metodunun Bazı 3+1 Boyutlu Lineer Olmayan Oluşum Denklemlerine Uygulanması”, Karaelmas Fen ve Mühendislik Dergisi, vol. 8, no. 2, pp. 433–437, 2018.
ISNAD Ünsal, Ömer. “Genişletilmiş Dönüştürülmüş Rasyonel Fonksiyon Metodunun Bazı 3+1 Boyutlu Lineer Olmayan Oluşum Denklemlerine Uygulanması”. Karaelmas Fen ve Mühendislik Dergisi 8/2 (June 2018), 433-437.
JAMA Ünsal Ö. Genişletilmiş Dönüştürülmüş Rasyonel Fonksiyon Metodunun Bazı 3+1 Boyutlu Lineer Olmayan Oluşum Denklemlerine Uygulanması. Karaelmas Fen ve Mühendislik Dergisi. 2018;8:433–437.
MLA Ünsal, Ömer. “Genişletilmiş Dönüştürülmüş Rasyonel Fonksiyon Metodunun Bazı 3+1 Boyutlu Lineer Olmayan Oluşum Denklemlerine Uygulanması”. Karaelmas Fen Ve Mühendislik Dergisi, vol. 8, no. 2, 2018, pp. 433-7.
Vancouver Ünsal Ö. Genişletilmiş Dönüştürülmüş Rasyonel Fonksiyon Metodunun Bazı 3+1 Boyutlu Lineer Olmayan Oluşum Denklemlerine Uygulanması. Karaelmas Fen ve Mühendislik Dergisi. 2018;8(2):433-7.