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

Year 2018, Volume: 67 Issue: 2, 126 - 138, 01.08.2018

Yakup Yıldırım Emrullah Yaşar

Abstract

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

Keywords

(2+1)-dimensional non-local Ito equation, Wronskian method, Soliton

References

• 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 : [e-mail] 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 : [e-mail] ORCID Address:
• http://orcid.org/0000-0003-4732-5753