Modified exponential function method for the KP-BBM equation

Volume 6, Issue 1, pp 1--7 http://dx.doi.org/10.22436/mns.06.01.01

Publication Date: April 09, 2020 Submission Date: May 06, 2019 Revision Date: October 29, 2019 Accteptance Date: December 04, 2019

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1554 Downloads
• 2988 Views

Authors

Tolga Akturk - Department of Mathematics and Science Education, Faculty of Education, Ordu University, Turkey. Gulnur Yel - Faculty of Educational Sciences, Final International University, Kyrenia, Mersin 10, Turkey.

Abstract

In this study, the travelling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona- Mahony equation were obtained by using modified exponential function method. This method provides the solution of nonlinear partial differential equation by using exponential function. The submitted solutions are implied in terms of the hyperbolic functions, trigonometric functions. The 2D and 3D graphics and contour simulations of these solution functions were obtained by using computational program.

Share and Cite

Keywords

• The nonlinear equations
• Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation (KP-BBM)
• the modified exponential function method (MEFM)

MSC

•  35Q99
•  35C07

References

• [1] T. Akturk, Y. Gurefe, H. Bulut, New function method to the (n + 1)-dimensional nonlinear problems, Int. J. Optim. Control. Theor. Appl. IJOCTA, 7 (2017), 234--239
  • View Article


• [2] T. Akturk, Y. Gurefe, H. Bulut, An application of the new function method to the Zhiber-Shabat equation, Int. J. Optim. Control. Theor. Appl. IJOCTA, 7 (2017), 271--274
  • View Article


• [3] Z. Avazzadeh, M. H. Heydari, C. Cattani, Legendre wavelets for fractional partial integro-differential viscoelastic equations with weakly singular kernels, The European Physical Journal Plus, 134 (2019), 13 pages
  • View Article


• [4] H. M. Baskonus, New acoustic wave behaviors to the Davey-Stewartson equation with power-law nonlinearity arising in fluid dynamics, Nonlinear Dynam., 86 (2016), 177--183
  • View Article


• [5] H. M. Baskonus, New complex and hyperbolic function solutions to the generalized double combined Sinh-Cosh-Gordon equation, AIP Conf. Proc., 1798 (2017), 1--9
  • View Article


• [6] H. M. Baskonus, Complex soliton solutions to the Gilson-Pickering model, Axioms, 8 (2019), 14 pages
  • View Article


• [7] H. M. Baskonus, H. Bulut, On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method, Waves Random Complex Media, 25 (2015), 720--728
  • View Article


• [8] H. M. Baskonus, H. Bulut, A. Atangana, On the complex and hyperbolic structures of the longitudinal wave equation in a magneto-electro-elastic circular rod, Smart Materials and Structures, 25 (2016), 8 pages
  • View Article


• [9] H. M. Baskonus, H. Bulut, T. A. Sulaiman, Investigation of various travelling wave solutions to the extended (2 + 1)- dimensional quantum ZK equation, Eur. Phys. J. Plus, 132 (2017), 8 pages
  • View Article


• [10] H. M. Baskonus, H. Bulut, T. A. Sulaiman, New complex hyperbolic structures to the Lonngren-wave equation by using sine-Gordon expansion method, Appl. Math. Nonlinear Sci., 4 (2019), 141--150
  • View Article


• [11] H. M. Baskonus, T. A. Sulaiman, H. Bulut, Bright, dark optical and other solitons to the generalized higher-order NLSE in optical Fibers, Optical and Quantum Electronics, 50 (2018), 12 pages
  • View Article


• [12] J. L. Bona, On solitary waves and their role in the evolution of long waves, Applications of Nonlinear Analysis in the Physical Sciences, 1981 (1981), 183--205
  • View Article


• [13] H. Bulut, T. Akturk, Y. Gurefe, Travelling wave solutions of the (N + 1)-dimensional sine-cosine-Gordon equation, AIP Conf. Proc., 1637 (2014), 145--149
  • View Article


• [14] H. Bulut, G. Yel, H. M. Baskonus, An application of improved Bernoulli sub-equation function method to the nonlinear time-fractional burgers equation, Turk. J. Math. Comput. Sci., 5 (2016), 1--7
  • View Article


• [15] C. Cattani, Multiscale analysis of wave propagation in composite materials, Math. Model. Anal., 8 (2003), 267--282
  • View Article


• [16] C. Cattani, Harmonic wavelet solutions of the Schrodinger equation, Int. J. Fluid Mech. Res., 30 (2003), 463--472
  • View Article


• [17] C. Cattani, T. A. Sulaiman, H. M. Baskonus, H. Bulut, Solitons in an inhomogeneous Murnaghan’s rod, Eur. Phys. J. Plus, 133 (2018), 11 pages
  • View Article


• [18] C. Cattani, T. A. Sulaiman, H. M. Baskonus, H. Bulut, On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfel’d-Sokolov systems, Opt. Quant. Electron., 50 (2018), 11 pages
  • View Article


• [19] Y. Chen, Z. Yan, New exact solutions of (2 + 1)-dimensional Gardner equation via the new sine-Gordon equation expansion method, Chaos Solitons Fractals, 26 (2005), 399--406
  • View Article


• [20] A. Ciancio, H. M. Baskonus, T. A. Sulaiman, H. Bulut, New structural dynamics of isolated waves via the coupled nonlinear Maccari’s system with complex structure, Indian J. Phys., 92 (2018), 1281--1290
  • View Article


• [21] F. Dusunceli, New exponential and complex traveling wave solutions to the Konopelchenko-Dubrovsky model, Adv. Math. Phys., 2019 (2019), 9 pages
  • View Article


• [22] F. Dusunceli, Solutions for the Drinfeld-Sokolov equation using an IBSEFM method, MSU J. of Sci., 6 (2018), 505--510
  • View Article


• [23] F. Dusunceli, New exact solutions for the (3+ 1)-dimensional B-type Kadomtsev-Petviashvili equation, Erzincan University Journal of Science and Technology, 12 (2019), 463--468
  • View Article


• [24] S. M. El-Shaboury, M. K. Ammar, W. M. Yousef, Analytical solutions of the relative orbital motion in unperturbed and in J2-perturbed elliptic orbits, Appl. Math. Nonlinear Sci., 2 (2017), 403--414
  • View Article


• [25] E. I. Eskitas¸c¸ioglu, M. B. Aktas, H. M. Baskonus, New complex and hyperbolic forms for Ablowitz-Kaup-Newell-Segur wave equation with fourth order, Appl. Math. Nonlinear Sci., 4 (2019), 105--112
  • View Article


• [26] J. H. He, X. H .Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fractals, 30 (2006), 700--708
  • View Article


• [27] M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek Ghaini, C. Cattani, A computational method for solving stochastic Ito-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions, J. Comput. Phys., 270 (2014), 402--415
  • View Article


• [28] B. B. Kadomtsev, V. I. Petviashvili, On the stability of solitary waves in weakly dispersing media, In Sov. Phys. Dokl., 15 (1970), 539--541
  • View Article


• [29] C. M. Khalique, I. E. Mhlanga, Travelling waves and conservation laws of a (2 + 1)-dimensional coupling system with Korteweg-de Vries equation, Appl. Math. Nonlinear Sci., 3 (2018), 241--253
  • View Article


• [30] N. A. Kudryashov, One method for finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 2248--2253
  • View Article


• [31] C. S. Liu, Trial equation method and its applications to nonlinear evolution equations, Acta Phys. Sinica, 54 (2005), 2505--2509
  • View Article


• [32] S. Micu, On the controllability of the linearized Benjamin-Bona-Mahony equation, SIAM J. Control Optim., 39 (2001), 1677--1696
  • View Article


• [33] P. K. Pandey, A new computational algorithm for the solution of second order initial value problems in ordinary differential equations, Appl. Math. Nonlinear Sci., 3 (2018), 167--173
  • View Article


• [34] Y. Pandir, Y. Gurefe, U. Kadak, E. Misirli, Classification of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstr. Appl. Anal., 2012 (2012), 16 pages
  • View Article


• [35] Y. Pandir, Y. Gurefe, E. Misirli, A new approach to Kudryashov’s method for solving some nonlinear physical models, Int. J. Phys. Sci., 7 (2012), 2860--2866
  • View Article


• [36] D. Rani, V. Mishra, C. Cattani, Numerical inversion of Laplace transform based on Bernstein operational matrix, Math. Methods Appl. Sci., 41 (2018), 9231--9243
  • View Article


• [37] D. Rani, V. Mishra, C. Cattani, Numerical inverse Laplace transform for solving a class of fractional differential equations, Symmetry, 11 (2019), 20 pages
  • View Article


• [38] J. J. Rushchitsky, C. Cattani, E. V. Terletskaya, Wavelet analysis of the evolution of a solitary wave in a composite material, Int. Appl. Mech., 40 (2004), 311--318
  • View Article


• [39] G. Shen, Y. Sun, Y. Xiong, New travelling-wave solutions for Dodd-Bullough equation, J. Appl. Math., 2013 (2013), 5 pages
  • View Article


• [40] Y. Sun, New travelling wave solutions for Sine-Gordon equation, J. Appl. Math., 2014 (2014), 4 pages
  • View Article


• [41] T. A. Sulaiman, H. Bulut, A. Yokus, H. M. Baskonus, On the exact and numerical solutions to the coupled Boussinesq equation arising in ocean engineering, Indian J. Phys., 93 (2019), 647--656
  • View Article


• [42] T. A. Sulaiman, A. Yokus, N. Gulluoglu, H. M. Baskonus, Regarding the Numerical and Stability Analysis of the Sharma-Tasso-Olver Equation, ITM Web Conf., 22 (2018), 9 pages
  • View Article


• [43] F. Xu, Application of Exp-function method to symmetric regularized long wave (SRLW) equation, Phys. Lett., 372 (2008), 252--257
  • View Article


• [44] X. F. Yang, Z. C. Deng, Y. Wei, A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application, Adv. Difference Equ., 2015 (2015), 17 pages
  • View Article


• [45] G. Yel, H. M. Baskonus, H. Bulut, Novel archetypes of new coupled Konno–Oono equation by using sine–Gordon expansion method, Opt. Quant. Electron., 49 (2017), 10 pages
  • View Article


• [46] G. Yel, H. M. Baskonus, H. Bulut, Regarding on the some novel exponential travelling wave solutions to the Wu-Zhang system arising in nonlinear water wave model, Indian J. Phys., 93 (2019), 1031--1039
  • View Article


• [47] A. Yokus, Comparison of Caputo and conformable derivatives for time-fractional Korteweg–de Vries equation via the finite difference method, Internat. J. Modern Phys., 32 (2018), 12 pages
  • View Article


• [48] A. Yokus, S. Gulbahar, Numerical solutions with linearization techniques of the fractional Harry Dym equation, Appl. Math. Nonlinear Sci., 4 (2019), 35--41
  • View Article


• [49] A. Yokus, T. A. Sulaiman, M. T. Gulluoglu, H. Bulut, Stability analysis, numerical and exact solutions of the (1 + 1)- dimensional NDMBBM equation, ITM Web Conf., 22 (2018), 10 pages
  • View Article


• [50] A. Yokus, M. Tuz, An application of a new version of (G′/G)-expansion method, In AIP Conf. Proc., 1798 (2017), 7 pages
  • View Article


• [51] A. M. Wazwaz, The extended tanh method for new compact and noncompact solutions for the KP-BBM and the ZK-BBM equations, Chaos Solitons Fractals, 38 (2008), 1505--1516
  • View Article