AIMS Mathematics, 2017, 2(3): 385-399. doi: 10.3934/Math.2017.3.385

Research article

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

The exact traveling wave solutions of a class of generalized Black-Scholes equation

School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

In this paper, the traveling wave solutions of a class of generalized Black-Scholes equation are considered. By using the first integral method and the G'/G-expansion method, several exact traveling wave solutions of the equation are obtained.
  Article Metrics


1. Fischer Black, Myron Scholes, The Pricing of Options and Corporate Liabilities, The Journal of Political Economy, 81 (1973), 637-654.    

2. Sunday O. Edeki, Olabisi O. Ugbebor and Enahoro A Owoloko, Analytical solutions of the Black-Scholes pricing model for European option valuation via a projected differential transformation method, Entropy, 17 (2015), 7510-7521.    

3. Erik Ekström, Johan Tysk, The Black-Scholes equation in stochastic volatility models, J. Math. Anal. Appl., 368 (2010), 498-507.    

4. Rubén Figueroa and Maria do Rosário Grossinho, On some nonlinear boundary value problems related to a Black-Scholes model with transaction costs, Boundary value problems, 2015.

5. Zhaosheng Feng, The first-integral method to study the Burgers-Korteweg-de Vries equation, Journal of Physics A: Mathematical and General, 35 (2002), 343-349.    

6. M. Mirzazadeha, Anjan Biswasb, Optical solitons with spatio-temporal dispersion by first integral approach and functional variable method, Optik, 125 (2014) 5467-5475.

7. Bin Lu, Hongqing Zhang and Fuding Xie, Travelling wave solutions of nonlinear partial equations by using the first integral method, Applied Mathematics and Computation, 216 (2010), 1329-1336.    

8. Filiz Tascan, Ahmet Bekir and Murat Koparan, Travelling wave solutions of nonlinear evolution equations by using the first integral method, Commun Nonlinear Sci Numer Simulat, 14 (2009), 1810-1815.    

9. Zhaosheng Feng, Xiaohui Wang, The first method to the two-dimensional Burgers-Korteweg-de Vries equation, Physics Letters A, 308 (2003), 173-178.    

10. Zhaosheng Feng, On explicit exact solutions to the compound Burgers-KdV equation, Physics Letters A, 293 (2002), 57-66.    

11. Zhaosheng Feng, Exact solution to an approximate sine-Gordon equation in (n+1)-dimensional space, Physics Letters A, 302 (2002), 64-76.    

12. Yanxia Hu, Weiping Gao, Exact and explicit solutions of a coupled nonlinear Schrödinger type equation, Asian Journal of Mathematics and Computer Research, 9 (2016), 240-252.

13. Mingliang Wang, Xiangzheng Li and Jinliang Zhang, The G'/G-expansion method and travling wave solutions of nonlinear evolution equations in mathematics physics, Phys.Lett.A, 372 (2008), 417-423.    

14. M.Mirzazadeha, M.Eslamib, Daniela Milovicc and Anjan Biswasd, Topological solitons of resonant nonlinear Schödinger's equation with dual-power law nonlinearity by G'/G-expansion technique, Optik, 125 (2014), 5480-5489.    

15. E.M.E. Zayed, The G'/G-expansion method and its applications to some nonlinear evolution equations in the mathematical physics, J. Appl. Math. Comput., 30 (2009), 89-103.    

16. Sheng Zhang, Jinglin Tong and Wei Wang, A generalized G'/G-expansion method for the mKdV equation with variable coeffcients, Physics Letters A, 372 (2008), 2254-2257.    

17. Turgut Öziş, İsmail Aslan, Application of the G'/G-expansion method to Kawahara type equations using symbolic computation Applied Mathematics and Computation, 216 (2010), 2360-2365.

18. Lingxiao Li, Mingliang Wang, The G'/G-expansion method and travelling wave solutions for a higher-order nonlinear schrödinger equation Applied Mathematics and Computation, 208 (2009), 440-445.

19. Hua Gao, Rongxia Zhao , New application of the G'/G-expansion method to higher-order nonlinear equations, Elsevier Science Inc., 2009.

Copyright Info: © 2017, Yanxia Hu, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved