Some novel exponential function structures to the Cahn–Allen equation

References

• Altan Koç, D., Baskonus, H. M., & Bulut, H. (2016, March 3–6). Dark and new travelling wave solutions to the nonlinear evolution equation. In 1st International Symposium on Computational Mathematics and Engineering Sciences, La Faculté des Sciences et Techniques d’Errachidia.
   Google Scholar
• Atangana, A. (2013a). A note on the triple Laplace transform and its applications to some kind of third-order differential equation, Abstract and Applied Analysis, 10 p., Article ID 769102.
   Google Scholar
• Atangana, A. (2013b). On the solution of an acoustic wave equation with variable-order derivative loss operator. Advances in Difference Equations, 2013, 167.10.1186/1687-1847-2013-167
   Web of Science ®Google Scholar
• Atangana, A., & Alabaraoye, E. (2013). Exact solutions fractional heat-like and wave-like equations with variable coefficients. Scientific Reports, 2(633).
   Google Scholar
• Atangana, A., & Bildik, N. (2013). Approximate solution of tuberculosis disease population dynamics model. Abstract and Applied Analysis, 2013, 8 p., Article ID 759801.
   Google Scholar
• Atangana, A., & Oukouomi Noutchie, S. C. (2013). Two-dimension hydrodynamic dispersion equation with seepage velocity and dispersion coefficient as function of space and time, Abstract and Applied Analysis, 2013, 7 p., Article ID 206942.
   Google Scholar
• Baskonus, H. M. (2016). New acoustic wave behaviours to the Davey-Stewartson equation with power-law nonlinearity arising in fluid dynamics. Nonlinear Dynamics, 1–7. doi:10.1007/s11071-016-2880-4
   Web of Science ®Google Scholar
• Baskonus, H. M., & Bulut, H. (2015). On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method. Waves in Random and Complex Media, 25, 720–728.10.1080/17455030.2015.1080392
   Web of Science ®Google Scholar
• Baskonus, H. M., & Bulut, H. (2016a). Exponential prototype structures for (2+1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics. Waves in Random and Complex Media, 26, 201–208.
   Web of Science ®Google Scholar
• Baskonus, H. M., & Bulut, H. (2016b, March 03–06). On the Complex Analytical Solutions for the Fractional Nonlinear Double sinh-Poisson Equation. In 1st International Symposium on Computational Mathematics and Engineering Sciences, Errichidia.
   Google Scholar
• Baskonus, H. M., Bulut, H., & Atangana, A. (2016). On the Complex and Hyperbolic Structures of Longitudinal Wave Equation in a Magneto-Electro-Elastic Circular Rod, Smart Materials and Structures, 25(3), 8 pp, 035022.
   Web of Science ®Google Scholar
• Baskonus, H. M., Bulut, H., & Kayhan, M. (2015, August 25–28). Regarding analytical prototype studies for the generalized nonlinear Pochhammer-Chree equation. In International Conference on Pure and Applied Mathematics (ICPAM 2015), Van.
   Google Scholar
• Baumann, G. (1978). James D. Bond, A novel molecular interpretation of the Hodgkin-Huxley model of electrical excitability, Mathematical Biosciences, 39, 291–297.
   Google Scholar
• Bulut, H., & Baskonus, H. M. (2016, March 03–06). New complex hyperbolic function solutions for the (2+1)-dimensional dispersive long water–wave system. In 1st International Symposium on Computational Mathematics and Engineering Sciences, Errichidia.
   Google Scholar
• Ciancio, A. (2007). Analysis of time series with wavelets. International Journal of Wavelets, Multiresolution and Information Processing, 5, 241–256.10.1142/S0219691307001744
   Web of Science ®Google Scholar
• Ciancio, A., Ciancio, V., & Farsaci, F. (2007). Wave propagation in media obeying a thermo viscoan elastic model. University Politehnica of Bucharest Scientific Bullettin, Series A: Applied Mathematics and Physics, 69, 69–79.
   Google Scholar
• Ciancio, V., Ciancio, A., & Farsaci, F. (2008). On general properties of phenomenological and state coefficients for isotropic viscoanelastic media. Physica B: Condensed Matter, 403, 3221–3227.10.1016/j.physb.2008.04.021
   Web of Science ®Google Scholar
• Ciancio, A., & Quartarone, A. (2013). A hybrid model for tumor-immune competition, University Politehnica of Bucharest Scientific Bullettin, Series A: Applied Mathematics and Physics, 75, 125–136.
   Google Scholar
• Hedayati, R., Jafari, S., & Batebi, S. (2016). Free-electron dynamics and gain in a free-electron laser based on the laser-pumped wiggler. Optik - International Journal for Light and Electron Optics, 127, 4639–4644.10.1016/j.ijleo.2015.09.227
   Google Scholar
• Luo, M., Xie, H., Xie, L., Cai, P., & Gu, L. (2014). A robust and real-time vascular intervention simulation based on Kirchhoff elastic rod. Computerized Medical Imaging and Graphics, 38, 735–743.10.1016/j.compmedimag.2014.08.002
   PubMed Web of Science ®Google Scholar
• Manafian, J. (2016). Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan(Φ(ξ)/2)-expansion method. Optik - International Journal for Light and Electron Optics, 127, 4222–4245.10.1016/j.ijleo.2016.01.078
   Google Scholar
• Manafian, J., & Lakestani, M. (2016a). Application of tan(ϕ/2)-expansion method for solving the Biswas-Milovic equation for Kerr law nonlinearity. Optik - International Journal for Light and Electron Optics, 127, 2040–2054.10.1016/j.ijleo.2015.11.078
   Google Scholar
• Manafian, J., & Lakestani, M. (2016b). Abundant soliton solutions for the Kundu-Eckhaus equation via tan(ϕ(ξ))-expansion method. Optik - International Journal for Light and Electron Optics, 127, 5543–5551.
   Google Scholar
• Miller, J. T., Su, T., Pabon, J., Wicks, N., Bertoldi, K., & Reis, P. M. (2015). Buckling of a thin elastic rod inside a horizontal cylindrical constraint. Extreme Mechanics Letters, 3, 36–44.10.1016/j.eml.2015.03.002
   Web of Science ®Google Scholar
• Murphy, J. G. (2015). The stability of thin, stretched and twisted elastic rods. International Journal of Non-Linear Mechanics, 68, 96–100.10.1016/j.ijnonlinmec.2014.05.018
   Web of Science ®Google Scholar
• Özpinar, F., Baskonus, H. M., & Bulut, H. (2015). On the Complex and Hyperbolic Structures for the (2+1)-Dimensional Boussinesq Water Equation. Entropy, 17, 8267–8277.10.3390/e17127878
   Web of Science ®Google Scholar
• Rodríguez-Arós, Á., & Viaño, J. M. (2015). A bending–stretching model in adhesive contact for elastic rods obtained by using asymptotic methods. Nonlinear Analysis: Real World Applications, 22, 632–644.10.1016/j.nonrwa.2014.08.004
   Web of Science ®Google Scholar
• Salik, M., Hanif, M., Wang, J., & Zhang, X. Q. (2016). Laser based diagnostics of slaked lime plasma. Optik - International Journal for Light and Electron Optics, 127, 1940–1945.10.1016/j.ijleo.2015.11.112
   Google Scholar
• Taşcan, F., & Bekir, A. (2009). Travelling wave solutions of the Cahn-Allen equation by using first integral method. Applied Mathematics and Computation, 207, 279–282.10.1016/j.amc.2008.10.031
   Web of Science ®Google Scholar
• Tseng, S., & Hsu, J. P. (1990). A stochastic analysis of the repair of radiation-induced DNA double-strand breaks. Mathematical Biosciences, 100, 21–31.10.1016/0025-5564(90)90045-Z
   PubMed Web of Science ®Google Scholar
• Umetani, N., Schmidt, R., & Stam, J. (2014). Position-based elastic rods. Symposium on Computer Animation, 2014, 1–10.
   Google Scholar
• Zheng, B. (2012). Application of A generalized Bernoulli sub-ODE method for finding traveling solutions of some nonlinear equations. WSEAS Transactions on Mathematics, 7, 618–626.
   Google Scholar