SITEM for the Conformable Space-Time fractional (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov Equations

Year 2019, Volume: 2 Issue: 3, 155 - 162, 26.12.2019

Handan Yaslan , Ayşe Girgin

https://doi.org/10.33187/jmsm.558879

Abstract

In the present paper, new analytical solutions for the space-time fractional (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) equations are obtained by using the simplified $\tan(\frac{\phi (\xi) }{2})$-expansion method (SITEM)

Keywords

Conformable derivative, Simplified $\tan(\frac{\phi (\xi) }{2})$-expansion method (SITEM), Space-time fractional (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations

References

• [1] Y. Y. Wang, Y. P. Zhang, C. Q. Dai, Re-study on localized structures based on variable separation solutions from the modified tanh-function method, Nonlinear Dyn, 83 (2016), 1331-1339.
• [2] D. J. Ding, D. Q. Jin, C. Q. Dat, Analytical Solutions of Differential-Difference Sine-Gordon Equation, Thermal Science, 21 (2017), 1701-1705.
• [3] C. Q. Dai, J. Liu, Y. Fan, D. G. Yu, Two-dimensional localized Peregrine solution and breather excited in a variable-coefficient nonlinear Schrodinger equation with partial nonlocality, Nonlinear Dyn., 88 (2017), 1373-1383.
• [4] C. Q. Dai, G. Q. Zhou, Exotic interactions between solitons of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, Chinese Phys., 16 (2007), 1201-1208.
• [5] T. Hong, Y. Z. Wang, Y. S. Huo, Bogoliubov quasiparticles carried by dark solitonic excitations in nonuniform Bose Einstein condensates, Chin. Phys. Lett., 15 (1998), 550-552.
• [6] G. C. Das, Explosion of soliton in a multicomponent plasma, Phys. Plasmas, 4 (1997), 2095-2100.
• [7] S. Y. Lou, A direct perturbation method: Nonlinear Schrodinger equation with loss, Chin. Phys. Lett., 16 (1999), 659-661.
• [8] C. Q. Dai, S. S. Wu, X. Cen, New exact solutions of the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, Int. J. Theor. Phys., 47 (2008), 1286-1293.
• [9] C. Q. Dai, Y. Y. Wang, New variable separation solutions of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselo system, Nonlinear Anal., 71 (2009), 1496-1503.
• [10] S. Zhang, T. C. Xia, A generalized auxiliary equation method and its application to (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equations, J. Phys. A: Math. Theor., 40 (2007), 227-248.
• [11] A. Borhanifar, M. M. Kabir, L. M. Vahdat, New periodic and soliton wave solutions for the generalized Zakharov system and (2 + 1)-dimensional Nizhnik-Novikov-Veselov system, Chaos Soliton Fractals, 42 (2009), 1646-1654.
• [12] C. Deng, New abundant exact solutions for the (2 + 1)-dimensional generalized Nizhnik-Novikov-Veselo system, Commun. Nonlinear Sci. Numer. Simula., 15 (2010), 3349-3357.
• [13] E. Yusufoglu, A. Bekir, Exact solutions of coupled nonlinear evolution equations, Chaos Soliton Fractals, 37 (2008), 842-848.
• [14] Y. J. Ren, H. Q. Zhang, A generalized F-expansion method to find abundant families of Jacobi Elliptic Function solutions of the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equation, Chaos Soliton Fractals, 27 (2006), 959-979.
• [15] J. Tang, F. Han, M. Zhao, W. Fu, Travelling wave solutions for the (2 + 1) dimensional Nizhnik-Novikov-Veselov equation, Appl. Math. Comput., 218 (2012), 11083-11088.
• [16] Y. Chen, Z. Z. Dong, Symmetry reduction and exact solutions of the generalized Nizhnik-Novikov-Veselov equation, Nonlinear Anal., 71 (2009), 810-817.
• [17] A. M. Wazwaz, Structures of multiple soliton solutions of the generalized, asymmetric and modified Nizhnik-Novikov-Veselov equations, Appl. Math. Comput., 218 (2012), 11344-11349.
• [18] L. M. Yan, F. S. Xu, Generalized Exp-Function Method for Non-Linear Space-Time Fractional Differential Equations, Thermal Science, 18 (2014), 1573-1576.
• [19] O. Guner, New travelling wave solutions for fractional regularized long-wave equation and fractional coupled Nizhnik-Novikov-Veselov equation, J. Optim. Control Theor. Appl., 8 (2018), 63-72.
• [20] Y. Liu, L. Yan, SSolutions of Fractional Konopelchenko-Dubrovsky and Nizhnik-Novikov-Veselov Equations Using a Generalized Fractional Subequation Method, Abstr. Appl. Anal., 2013 (2013), Article ID 839613, 7 pages, doi:10.1155/2013/839613.
• [21] O. Tasbozan, Y. Cenesiz, A. Kurt, D. Baleanu, New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method, Open Phys., 15 (2017), 647-651.
• [22] A. Kurt, O. Tasbozan, D. Baleanu, New solutions for conformable fractional Nizhnik- Novikov-Veselov system via G0=G expansion method and homotopy analysis methods, Opt. Quant. Electron., 49(333) (2017), 1-16.
• [23] J. Manafian, M. Foroutan, Application of tan(f(x )=2)-expansion method for the time-fractional Kuramoto-Sivashinsky equation, Opt. Quant. Electron., 49(272) (2017), 1-18.
• [24] J. Manafian, M. Lakestani, Optical soliton solutions for the Gerdjikov-Ivanov model via tan(f(x )=2)-expansion method, Optik, 127 (2016), 9603-9620.
• [25] J. Manafian, M. F. Aghdaei, M. Zadahmad, Analytic study of sixth-order thin-film equation by tan(f(x )=2)-expansion method, Opt. Quant. Electron., 48 (2016), 410-424.
• [26] H. Liu, T. Zhang, A note on the improved tan(f(x )=2)-expansion method, Optik, 131 (2017), 273-278.
• [27] H. C. Yaslan, A. Girgin, Sitem for the conformable space-time fractional coupled kd equations, J. Eng. Tech. Appl. Sci., 3 (2018), 223-233.
• [28] R. Khalil, M. A. Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65-70.
• [29] M. Boiti, J. J. P. Leon, M. Manna, F. Pempinelli, On the spectral transform of a Korteweg-de Vries equation in two spatial dimensions, Inverse Probl., 2 (1986), 271-279.