BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 67 Sayı: 2, 126 - 138, 01.08.2018

Öz

Kaynakça

  • Ablowitz, M. J., Segur, H., Solitons and the inverse scattering transform (Vol. 4, pp. x+-425). Philadelphia: Siam, 1981.
  • Adem, A. R., The generalized (1 + 1)-dimensional and (2 + 1)-dimensional Ito equations: multiple exp-function algorithm and multiple wave solutions. Computers & Mathematics with Applications. (2016), 71(6), 1248-1258.
  • Adomian, G., Solving frontier problems of physics: the decomposition method. Vol. 60. Springer Science & Business Media, 2013.
  • Ebadi, G., Kara, A. H., Petkovic, M. D., Yildirim, A. and Biswas, A. Solitons and conserved quantities of the Ito equation. Proceedings of the Romanian Academy, Series A.(2012), 13(3), 215-224.
  • Freeman N.C and Nimmo J.J.C., Soliton solutions of the Korteweg-de Vries and Kadomtsev- Petviashvili equations: the Wronskian technique. Phys. Lett. A. (1983), 95, 1-3.
  • Gandarias, M. L., and Chaudry M. K., Symmetries, solutions and conservation laws of a class of nonlinear dispersive wave equations. Communications in Nonlinear Science and Numerical Simulation 32 (2016): 114-121.
  • He, J.H., Variational iteration method–a kind of non-linear analytical technique: some ex- amples. International journal of non-linear mechanics. (1999), 34.4, 699-708.
  • Hirota, R., The direct method in soliton theory. Vol. 155. Cambridge University Press, 2004. [9] Ito M., An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher order. J. Phys. Soc. Japan. (1980), 49 (2), 771–778.
  • Li C.X., Ma W.X., Liu X.J. and Zeng Y.B., Wronskian solutions of the Boussinesq equation solitons, negatons, positons and complexitons, Inverse Problems 23 (2007) 279 296.
  • Ma, W. X., Wronskians, generalized Wronskians and solutions to the Korteweg–de Vries equation. Chaos, Solitons & Fractals, (2004) 19(1), 163-170.
  • Ma, W. X. and You, Y., Solving the Korteweg-de Vries equation by its bilinear form: Wron- skian solutions. Transactions of the American mathematical society, (2005) 357(5), 1753- 1778.
  • Ma, W. X. and Maruno, K. I., Complexiton solutions of the Toda lattice equation. Physica A: Statistical Mechanics and its Applications, (2004) 343, 219-237.
  • Momani, S and Salah A., Application of He’s variational iteration method to Helmholtz equation. Chaos, Solitons & Fractals. (2006), 27.5, 1119-1123.
  • Nimmo J.J.C. and Freeman N.C., A method of obtaining the N-soliton solution of the Boussi- nesq equation in terms of a Wronskian. Phys. Lett. A . (1983), 95, 4-6.
  • Su, J., New exact solutions for the (3 + 1)-dimensional generalized BKP equation, preprint. [17] Tang, Y., Ma, W. X., Xu, W. and Gao, L., Wronskian determinant solutions of the (3 + 1)- dimensional Jimbo–Miwa equation. Applied Mathematics and Computation. (2011), 217(21), 8722-8730.
  • Tian, S. F. and Zhang, H. Q., Riemann theta functions periodic wave solutions and ratio- nal characteristics for the (1 + 1)-dimensional and (2 + 1)-dimensional Ito equation. Chaos, Solitons & Fractals. (2013), 49 (2), 27-41.
  • Wazwaz, A.M., A sine-cosine method for handlingnonlinear wave equations. Mathematical and Computer modelling. (2004), 40.5 499-508.
  • Wazwaz, A.M., The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations. Chaos, Solitons & Fractals. (2008), 38.5, 1505-1516. [21] Wazwaz A. M., Multiple-soliton solutions for the generalized (1 + 1)-dimensional and the generalized (2+1)-dimensional Ito equations, Applied Mathematics and Computation. (2008), 202, 840–849.
  • Yong, C., Li B. and Zhang H. Q., Generalized Riccati equation expansion method and its application to the Bogoyavlenskii’s generalized breaking soliton equation. Chinese Physics. (2003), 12.9, 940.
  • Zayed, E. M. E. and Khaled A. G., The (G0=G)-expansion method for …nding traveling wave solutions of nonlinear partial diğerential equations in mathematical physics. Journal of Mathematical Physics. (2009), 50.1 013502. APA.
  • Current address : Yakup Yıldırım Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059, Bursa, TURKEY
  • E-mail address : yakupyildirim110@gmail.com ORCID Address:
  • Current address : Emrullah Ya¸sar (Corresponding author) Department of Mathematics, Fac- ulty of Arts and Sciences, Uludag University, 16059, Bursa, TURKEY
  • E-mail address : emrullah.yasar@gmail.com ORCID Address:
  • http://orcid.org/0000-0003-4732-5753

WRONSKIAN SOLUTIONS OF (2+1) DIMENSIONAL NON-LOCAL ITO EQUATION

Yıl 2018, Cilt: 67 Sayı: 2, 126 - 138, 01.08.2018

Öz

In this work, the Wronskian determinant technique is performed to(2+1)-dimensional non-local Ito equation in the bilinear form. First, we obtainsome su¢ cient conditions in order to show Wronskian determinant solves the(2+1)-dimensional non-local Ito equation. Second, rational solutions, solitonsolutions, positon solutions, negaton solutions and their interaction solutionswere deduced by using the Wronskian formulations

Kaynakça

  • Ablowitz, M. J., Segur, H., Solitons and the inverse scattering transform (Vol. 4, pp. x+-425). Philadelphia: Siam, 1981.
  • Adem, A. R., The generalized (1 + 1)-dimensional and (2 + 1)-dimensional Ito equations: multiple exp-function algorithm and multiple wave solutions. Computers & Mathematics with Applications. (2016), 71(6), 1248-1258.
  • Adomian, G., Solving frontier problems of physics: the decomposition method. Vol. 60. Springer Science & Business Media, 2013.
  • Ebadi, G., Kara, A. H., Petkovic, M. D., Yildirim, A. and Biswas, A. Solitons and conserved quantities of the Ito equation. Proceedings of the Romanian Academy, Series A.(2012), 13(3), 215-224.
  • Freeman N.C and Nimmo J.J.C., Soliton solutions of the Korteweg-de Vries and Kadomtsev- Petviashvili equations: the Wronskian technique. Phys. Lett. A. (1983), 95, 1-3.
  • Gandarias, M. L., and Chaudry M. K., Symmetries, solutions and conservation laws of a class of nonlinear dispersive wave equations. Communications in Nonlinear Science and Numerical Simulation 32 (2016): 114-121.
  • He, J.H., Variational iteration method–a kind of non-linear analytical technique: some ex- amples. International journal of non-linear mechanics. (1999), 34.4, 699-708.
  • Hirota, R., The direct method in soliton theory. Vol. 155. Cambridge University Press, 2004. [9] Ito M., An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher order. J. Phys. Soc. Japan. (1980), 49 (2), 771–778.
  • Li C.X., Ma W.X., Liu X.J. and Zeng Y.B., Wronskian solutions of the Boussinesq equation solitons, negatons, positons and complexitons, Inverse Problems 23 (2007) 279 296.
  • Ma, W. X., Wronskians, generalized Wronskians and solutions to the Korteweg–de Vries equation. Chaos, Solitons & Fractals, (2004) 19(1), 163-170.
  • Ma, W. X. and You, Y., Solving the Korteweg-de Vries equation by its bilinear form: Wron- skian solutions. Transactions of the American mathematical society, (2005) 357(5), 1753- 1778.
  • Ma, W. X. and Maruno, K. I., Complexiton solutions of the Toda lattice equation. Physica A: Statistical Mechanics and its Applications, (2004) 343, 219-237.
  • Momani, S and Salah A., Application of He’s variational iteration method to Helmholtz equation. Chaos, Solitons & Fractals. (2006), 27.5, 1119-1123.
  • Nimmo J.J.C. and Freeman N.C., A method of obtaining the N-soliton solution of the Boussi- nesq equation in terms of a Wronskian. Phys. Lett. A . (1983), 95, 4-6.
  • Su, J., New exact solutions for the (3 + 1)-dimensional generalized BKP equation, preprint. [17] Tang, Y., Ma, W. X., Xu, W. and Gao, L., Wronskian determinant solutions of the (3 + 1)- dimensional Jimbo–Miwa equation. Applied Mathematics and Computation. (2011), 217(21), 8722-8730.
  • Tian, S. F. and Zhang, H. Q., Riemann theta functions periodic wave solutions and ratio- nal characteristics for the (1 + 1)-dimensional and (2 + 1)-dimensional Ito equation. Chaos, Solitons & Fractals. (2013), 49 (2), 27-41.
  • Wazwaz, A.M., A sine-cosine method for handlingnonlinear wave equations. Mathematical and Computer modelling. (2004), 40.5 499-508.
  • Wazwaz, A.M., The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations. Chaos, Solitons & Fractals. (2008), 38.5, 1505-1516. [21] Wazwaz A. M., Multiple-soliton solutions for the generalized (1 + 1)-dimensional and the generalized (2+1)-dimensional Ito equations, Applied Mathematics and Computation. (2008), 202, 840–849.
  • Yong, C., Li B. and Zhang H. Q., Generalized Riccati equation expansion method and its application to the Bogoyavlenskii’s generalized breaking soliton equation. Chinese Physics. (2003), 12.9, 940.
  • Zayed, E. M. E. and Khaled A. G., The (G0=G)-expansion method for …nding traveling wave solutions of nonlinear partial diğerential equations in mathematical physics. Journal of Mathematical Physics. (2009), 50.1 013502. APA.
  • Current address : Yakup Yıldırım Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059, Bursa, TURKEY
  • E-mail address : yakupyildirim110@gmail.com ORCID Address:
  • Current address : Emrullah Ya¸sar (Corresponding author) Department of Mathematics, Fac- ulty of Arts and Sciences, Uludag University, 16059, Bursa, TURKEY
  • E-mail address : emrullah.yasar@gmail.com ORCID Address:
  • http://orcid.org/0000-0003-4732-5753
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA84ZU79GC
Bölüm Araştırma Makalesi
Yazarlar

Yakup Yıldırım Bu kişi benim

Emrullah Yaşar Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2018
Gönderilme Tarihi 1 Ağustos 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 67 Sayı: 2

Kaynak Göster

APA Yıldırım, Y., & Yaşar, E. (2018). WRONSKIAN SOLUTIONS OF (2+1) DIMENSIONAL NON-LOCAL ITO EQUATION. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(2), 126-138.
AMA Yıldırım Y, Yaşar E. WRONSKIAN SOLUTIONS OF (2+1) DIMENSIONAL NON-LOCAL ITO EQUATION. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2018;67(2):126-138.
Chicago Yıldırım, Yakup, ve Emrullah Yaşar. “WRONSKIAN SOLUTIONS OF (2+1) DIMENSIONAL NON-LOCAL ITO EQUATION”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, sy. 2 (Ağustos 2018): 126-38.
EndNote Yıldırım Y, Yaşar E (01 Ağustos 2018) WRONSKIAN SOLUTIONS OF (2+1) DIMENSIONAL NON-LOCAL ITO EQUATION. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 2 126–138.
IEEE Y. Yıldırım ve E. Yaşar, “WRONSKIAN SOLUTIONS OF (2+1) DIMENSIONAL NON-LOCAL ITO EQUATION”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 67, sy. 2, ss. 126–138, 2018.
ISNAD Yıldırım, Yakup - Yaşar, Emrullah. “WRONSKIAN SOLUTIONS OF (2+1) DIMENSIONAL NON-LOCAL ITO EQUATION”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/2 (Ağustos 2018), 126-138.
JAMA Yıldırım Y, Yaşar E. WRONSKIAN SOLUTIONS OF (2+1) DIMENSIONAL NON-LOCAL ITO EQUATION. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:126–138.
MLA Yıldırım, Yakup ve Emrullah Yaşar. “WRONSKIAN SOLUTIONS OF (2+1) DIMENSIONAL NON-LOCAL ITO EQUATION”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 67, sy. 2, 2018, ss. 126-38.
Vancouver Yıldırım Y, Yaşar E. WRONSKIAN SOLUTIONS OF (2+1) DIMENSIONAL NON-LOCAL ITO EQUATION. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(2):126-38.

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

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.