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On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional mKDV and mBBM Equations

Yıl 2021, Cilt: 25 Sayı: 1, 141 - 149, 01.02.2021

Hami Gündoğdu Ömer Faruk Gözükızıl

Öz

In this work, we consider (3+1) dimensional nonlinear partial differential equations, namely modified KdV and Benjamin-Bona-Mahony equations. Different types of solutions to these equations are derived by Jacobi elliptic sine function expansion method. Besides that, we introduce new types of solutions for two more modified forms of given equations. The gained solutions include exact, singular, periodic, and kink solutions. It is stated that some conditions related to the coefficients provide us with the existence of the gained solutions.

Anahtar Kelimeler

Elliptic sine function method (3+1)-Dimensional mKdV equation (3+1)-Dimensional mBBM equation

Kaynakça

  • Referans1 A. Wazwaz, “The extended tanh method for new solitons solutions for many forms of the fifth order KdV equations,” Appl. Math. Comput. Vol. 184, pp.1002-1014, 2007.
  • Referans2 A. Wazwaz, “New travelling wave solutions of different physical structures to generalized BBM equation,” Phys. Lett. A. Vol. 355, pp.358-362, 2006.
  • Referans3 A. Wazwaz and M. A. Helal, “Non-linear variants of the BBM equation with compact and noncompact physical structures,” Chaos. Solitons. Fractals. Vol. 26, pp.767-776, 2005.
  • Referans4 S. Elwakil, K. El-Labany, A. Zahran, and R. Sabry, “Modified extended tanh-function method for solving nonlinear partial differential equations,” Phys. Lett. A. Vol. 299, pp.179-88, 2002.
  • Referans5 C. T. Yan, “A simple transformation for nonlinear waves,” Phys. Lett. A. Vol. 224, pp. 77-84, 1996.
  • Referans6 T. Gao, and B. Tian, “Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations of mathematical physics,” Comput. Phys. Commun. Vol. 133, pp. 158-164, 2001.
  • Referans7 M. Wang, X. Li, and J. Zhang, “The (G’/G)- expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,” Phys. Lett. A. Vol. 372, pp. 417-423, 2008.
  • Referans8 J. He and L. Zhang, “Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method,” Phys. Lett. A. Vol. 371, pp. 1044-1047, 2008.
  • Referans9 H. Gündogdu and Ö. F. Gözükızıl, “Solving Benjamin-Bona-Mahony equation by usingˇ the sn-ns method and the tanh-coth method,” Math. Morav., Vol. 21, pp. 95-103, 2017.
  • Referans10 D. J. Korteweg and G. De Vries, “On the change of long waves advancing in a rectangular canal and a new type of long stationary wave,” Phil. Mag., Vol. 39, pp. 422-443, 1835.
  • Referans11 T. B. Benjamin, J. L. Bona, and J. J. Mahony, “Model equations for long waves in nonlinear dispersive systems,” Philos. Trans. R. Soc. London. Ser. A., Vol. 272, pp. 47-48, 1972.
  • Referans12 W. Hereman, “Shallow water waves and solitarywaves, Ecnyclopedis of Complexity and Systems Science,” Springer Verlag, Heibelberg, Germany, 2009.
  • Referans13 A. Wazwaz, “Exact soliton and kink solutions for new (3+1)-dimensional nonlinear modified equations of wave propagation,” Open. Eng., Vol. 7, pp. 169-174, 2017.
  • Referans14 S. K. Liu, Z. T. Fu, and S. D. Liu, “Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations,” Phys. Lett. A., Vol. 289, pp. 69-74, 2001.
  • Referans15 H. Gündogdu and Ö. F. Gözükızıl, “On different kinds of solutions to a simplified modified form of Camassa-Holm equation” J. Appl. Math. & Comput. Mech. Vol. 18, pp. 31-40, 2019.
  • Referans16 H. S. Alvaro, “Solving nonlinear partial differential equations by the sn-ns method,” Abstr. Appl. Analysis., Vol. 25, pp. 1-25, 2012.
  • Referans17 H. Zhang, “Extended Jacobi elliptic function expansion method and its applications,” Commun. Non. Sci. Numer. Simul., Vol. 12, pp. 627-635, 2007.
  • Referans18 H. Gündogdu and Ö. F. Gözükızıl, “On The New Type Of Solutions To Benney-Luke Equation,’’ Bol. Soc. Paran. Mat. doi:10.5269/bspm.41244.

Yıl 2021, Cilt: 25 Sayı: 1, 141 - 149, 01.02.2021

Hami Gündoğdu Ömer Faruk Gözükızıl

Öz

Kaynakça

  • Referans1 A. Wazwaz, “The extended tanh method for new solitons solutions for many forms of the fifth order KdV equations,” Appl. Math. Comput. Vol. 184, pp.1002-1014, 2007.
  • Referans2 A. Wazwaz, “New travelling wave solutions of different physical structures to generalized BBM equation,” Phys. Lett. A. Vol. 355, pp.358-362, 2006.
  • Referans3 A. Wazwaz and M. A. Helal, “Non-linear variants of the BBM equation with compact and noncompact physical structures,” Chaos. Solitons. Fractals. Vol. 26, pp.767-776, 2005.
  • Referans4 S. Elwakil, K. El-Labany, A. Zahran, and R. Sabry, “Modified extended tanh-function method for solving nonlinear partial differential equations,” Phys. Lett. A. Vol. 299, pp.179-88, 2002.
  • Referans5 C. T. Yan, “A simple transformation for nonlinear waves,” Phys. Lett. A. Vol. 224, pp. 77-84, 1996.
  • Referans6 T. Gao, and B. Tian, “Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations of mathematical physics,” Comput. Phys. Commun. Vol. 133, pp. 158-164, 2001.
  • Referans7 M. Wang, X. Li, and J. Zhang, “The (G’/G)- expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,” Phys. Lett. A. Vol. 372, pp. 417-423, 2008.
  • Referans8 J. He and L. Zhang, “Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method,” Phys. Lett. A. Vol. 371, pp. 1044-1047, 2008.
  • Referans9 H. Gündogdu and Ö. F. Gözükızıl, “Solving Benjamin-Bona-Mahony equation by usingˇ the sn-ns method and the tanh-coth method,” Math. Morav., Vol. 21, pp. 95-103, 2017.
  • Referans10 D. J. Korteweg and G. De Vries, “On the change of long waves advancing in a rectangular canal and a new type of long stationary wave,” Phil. Mag., Vol. 39, pp. 422-443, 1835.
  • Referans11 T. B. Benjamin, J. L. Bona, and J. J. Mahony, “Model equations for long waves in nonlinear dispersive systems,” Philos. Trans. R. Soc. London. Ser. A., Vol. 272, pp. 47-48, 1972.
  • Referans12 W. Hereman, “Shallow water waves and solitarywaves, Ecnyclopedis of Complexity and Systems Science,” Springer Verlag, Heibelberg, Germany, 2009.
  • Referans13 A. Wazwaz, “Exact soliton and kink solutions for new (3+1)-dimensional nonlinear modified equations of wave propagation,” Open. Eng., Vol. 7, pp. 169-174, 2017.
  • Referans14 S. K. Liu, Z. T. Fu, and S. D. Liu, “Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations,” Phys. Lett. A., Vol. 289, pp. 69-74, 2001.
  • Referans15 H. Gündogdu and Ö. F. Gözükızıl, “On different kinds of solutions to a simplified modified form of Camassa-Holm equation” J. Appl. Math. & Comput. Mech. Vol. 18, pp. 31-40, 2019.
  • Referans16 H. S. Alvaro, “Solving nonlinear partial differential equations by the sn-ns method,” Abstr. Appl. Analysis., Vol. 25, pp. 1-25, 2012.
  • Referans17 H. Zhang, “Extended Jacobi elliptic function expansion method and its applications,” Commun. Non. Sci. Numer. Simul., Vol. 12, pp. 627-635, 2007.
  • Referans18 H. Gündogdu and Ö. F. Gözükızıl, “On The New Type Of Solutions To Benney-Luke Equation,’’ Bol. Soc. Paran. Mat. doi:10.5269/bspm.41244.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Hami Gündoğdu 0000-0002-7042-1885

Ömer Faruk Gözükızıl 0000-0002-5975-6430

Yayımlanma Tarihi 1 Şubat 2021
Gönderilme Tarihi 26 Ekim 2020
Kabul Tarihi 26 Kasım 2020
Yayımlandığı Sayı Yıl 2021 Cilt: 25 Sayı: 1

Kaynak Göster

APA Gündoğdu, H., & Gözükızıl, Ö. F. (2021). On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional mKDV and mBBM Equations. Sakarya University Journal of Science, 25(1), 141-149.
AMA Gündoğdu H, Gözükızıl ÖF. On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional mKDV and mBBM Equations. SAUJS. Şubat 2021;25(1):141-149.
Chicago Gündoğdu, Hami, ve Ömer Faruk Gözükızıl. “On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional MKDV and MBBM Equations”. Sakarya University Journal of Science 25, sy. 1 (Şubat 2021): 141-49.
EndNote Gündoğdu H, Gözükızıl ÖF (01 Şubat 2021) On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional mKDV and mBBM Equations. Sakarya University Journal of Science 25 1 141–149.
IEEE H. Gündoğdu ve Ö. F. Gözükızıl, “On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional mKDV and mBBM Equations”, SAUJS, c. 25, sy. 1, ss. 141–149, 2021.
ISNAD Gündoğdu, Hami - Gözükızıl, Ömer Faruk. “On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional MKDV and MBBM Equations”. Sakarya University Journal of Science 25/1 (Şubat 2021), 141-149.
JAMA Gündoğdu H, Gözükızıl ÖF. On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional mKDV and mBBM Equations. SAUJS. 2021;25:141–149.
MLA Gündoğdu, Hami ve Ömer Faruk Gözükızıl. “On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional MKDV and MBBM Equations”. Sakarya University Journal of Science, c. 25, sy. 1, 2021, ss. 141-9.
Vancouver Gündoğdu H, Gözükızıl ÖF. On The Existence Conditions for New Kinds of Solutions to (3+1)-Dimensional mKDV and mBBM Equations. SAUJS. 2021;25(1):141-9.
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