Research Article

Construction of Exact Solutions to Partial Differential Equations with CRE Method

Volume: 2 Number: 2 June 27, 2019
Filiz Taşcan *, Arzu Akbulut
EN

Construction of Exact Solutions to Partial Differential Equations with CRE Method

Abstract

In this article, the consistent Riccati expansion (CRE) method is presented for constructing new exact solutions of (1+1) dimensional nonlinear dispersive modified Benjamin Bona Mahony (DMBBM) and mKdV-Burgers equations. The exact solutions obtained are composed of hyperbolic and exponential functions. The outcomes obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear partial differential equations.

Keywords

Partial differential equations,Exact solution,The consistent Riccati expansion

References

  1. [1] M. Kaplan, A. Akbulut, A. Bekir, Exact travelling wave solutions of the nonlinear evolution equations by auxiliary equation method, Z. Naturforsch A, 70 (2015), 969–974.
  2. [2] A. Bekir, A. Akbulut, M. Kaplan, Exact solutions of nonlinear evolution equations by using modified simple equation method, Int. J. Nonlinear Sci., 19 (2015), 159-164.
  3. [3] F. Tas¸can, A. Yakut, Conservation laws and exact solutions with symmetry reduction of nonlinear reaction diffusion equations, Int. J. Nonlinear Sci. Numer. Simul., 16 (2015), 191–196.
  4. [4] M. Ekici, M. Mirzazadeh, Q. Zhou, S. P. Moshokoa, A. Biswas, M. Belic, Solitons in optical metamaterials with fractional temporal evolution, Optik, 127 (2016), 10879-10897.
  5. [5] M. Mirzazadeh, M. Eslami, D. Milovic, A. Biswas, Topological solitons of resonant nonlinear Sch¨odinger’sequation with dual-power law nonlinearity by (G0=G)-expansion technique, Optik, 125 (19), (2014) 5480-5489.
  6. [6] Q. Feng, F. Meng, Explicit solutions for space-time fractional partial differential equations in mathematical physics by a new generalized fractional Jacobi elliptic equation-based sub-equation method, Optik, 127 (2016), 7450-7458.
  7. [7] A. Akbulut, M. Kaplan, F. Tas¸can, The investigation of exact solutions of nonlinear partial differential equations by using exp$\left(-\Phi \left( \xi \right) \right) $ method, Optik, 132 (2017), 382-387.
  8. [8] A. Biswas, M. Mirzazadeh, M. Eslami, D. Milovic, M. Belic, Solitons in optical metamaterials by functional variable method and first integral approach, Frequenz, 68 (11-12) (2014), 525-530.
  9. [9] B. Lu, The first integral method for some time fractional differential equations, J. Math. Anal. Appl., 395 (2012), 684-693.
  10. [10] H.M. Bas¸konus¸, H. Bulut , Analytical studies on the (1+1)-dimensional nonlinear Dispersive Modified Benjamin-Bona- Mahony equation defined by seismic sea waves, Waves Random Complex Media, doi:10.1080/17455030.1062577, 2015.
APA
Taşcan, F., & Akbulut, A. (2019). Construction of Exact Solutions to Partial Differential Equations with CRE Method. Communications in Advanced Mathematical Sciences, 2(2), 105-113. https://doi.org/10.33434/cams.486401
AMA
1.Taşcan F, Akbulut A. Construction of Exact Solutions to Partial Differential Equations with CRE Method. Communications in Advanced Mathematical Sciences. 2019;2(2):105-113. doi:10.33434/cams.486401
Chicago
Taşcan, Filiz, and Arzu Akbulut. 2019. “Construction of Exact Solutions to Partial Differential Equations With CRE Method”. Communications in Advanced Mathematical Sciences 2 (2): 105-13. https://doi.org/10.33434/cams.486401.
EndNote
Taşcan F, Akbulut A (June 1, 2019) Construction of Exact Solutions to Partial Differential Equations with CRE Method. Communications in Advanced Mathematical Sciences 2 2 105–113.
IEEE
[1]F. Taşcan and A. Akbulut, “Construction of Exact Solutions to Partial Differential Equations with CRE Method”, Communications in Advanced Mathematical Sciences, vol. 2, no. 2, pp. 105–113, June 2019, doi: 10.33434/cams.486401.
ISNAD
Taşcan, Filiz - Akbulut, Arzu. “Construction of Exact Solutions to Partial Differential Equations With CRE Method”. Communications in Advanced Mathematical Sciences 2/2 (June 1, 2019): 105-113. https://doi.org/10.33434/cams.486401.
JAMA
1.Taşcan F, Akbulut A. Construction of Exact Solutions to Partial Differential Equations with CRE Method. Communications in Advanced Mathematical Sciences. 2019;2:105–113.
MLA
Taşcan, Filiz, and Arzu Akbulut. “Construction of Exact Solutions to Partial Differential Equations With CRE Method”. Communications in Advanced Mathematical Sciences, vol. 2, no. 2, June 2019, pp. 105-13, doi:10.33434/cams.486401.
Vancouver
1.Filiz Taşcan, Arzu Akbulut. Construction of Exact Solutions to Partial Differential Equations with CRE Method. Communications in Advanced Mathematical Sciences. 2019 Jun. 1;2(2):105-13. doi:10.33434/cams.486401