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Application of simplest equation method to the (2+1)-dimensional nonlinear evolution equations

Year 2014, Volume: 2 Issue: 2, 64 - 68, 01.08.2014

Hossein Jafari Nematollah Kadkhoda

Abstract

In this paper, the simplest equation method has been used for finding the general exact solutions of nonlinear evolution equations that namely (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff( CBS) equation and (2+1)-dimensional breaking soliton equation (BS) when the simplest equation is the equation of Riccati

Keywords

Simplest equation method Calogero-Bogoyavlenskii- Schiff breaking soliton equation Riccati equation

References

  • Darvishi M., Najafi M., Najafi M. New application of EHTA for the generalized (2+1)-dimensional nonlinear evolution equations. 6(3), (2010)132-138.
  • Duranda M, Langevin D. Physicochemical approach to the theory of foam drainage. The European Physical Journal E 7(1), (2002) 35-44.
  • Fan E. Extended tanh-function method and its applications to nonlinear equations. physic letter A 277(4-5), (2000) 212-218.
  • Hone ANW. Painleve tests, singularity structure and integrability. Lect Notes Physics . (2009) . 767 245-277.
  • Jafari H, Kadkhoda N, Biswas A. The -expansion method for solutions of evolution equations from isothermal magnetostatic atmospheres. Journal of King Saud University – Science [In Press]. Kudryashov NA. On types of nonlinear integrable equations with exact solutions. physic letter A 155(4–5), (1991) 269-275.
  • Kudryashov NA. Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos, Solitons & Fractals 24(5), (2005) 1217-1231.
  • Kudryashov NALoguinova NB. Extended simplest equation method for nonlinear differential equations. Applied Mathematics and Computation 205 (1),(2008) 396-402.
  • Ostrovsky LANonlinear internal waves in a rotating ocean. Okeanologiya 1978;18:181-91 [in Russian] (Engl transl: Oceanology 18 119- 125) (1978).
  • Salehpour1 E, Jafari H, Kadkhoda N. Application of -expansion method to nonlinear Lienard equation. Indian Jour of Science and Technology 5(4), (2012) 2554-2556.
  • Wazwaz A.M. New solutions of distinct physical structures to highdimensional nonlinear evolution equations, Applied Mathematics and Computation 196(1) (2008) 363–370.
  • Wazwaz A.M. The (2+1) and (3+1)-Dimensional CBS Equations: Multiple Soliton Solutions and Multiple Singular Soliton Solutions, Zeitschrift fur Naturforschung A 65a, (2010) 173–181.
  • Wazwaz A.M Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations, Applied Mathematics and Computation 203(2), (2008) 592–597.
  • Wazwaz A.M. The tanh-coth method for solitons and kink solutions fornon-linear parabolic equations, Applied Mathematics and Computation 188(2), (2007) 1467-1475.
  • Wazwaz A.M. A sine-cosine method for handling nonlinear wave equations. Mathematical and Computer Modelling 40(5-6) ,(2004) 499- 50

Application of simplest equation method to the (2+1)-dimensional nonlinear evolution equations

Year 2014, Volume: 2 Issue: 2, 64 - 68, 01.08.2014

Hossein Jafari Nematollah Kadkhoda

Abstract

References

  • Darvishi M., Najafi M., Najafi M. New application of EHTA for the generalized (2+1)-dimensional nonlinear evolution equations. 6(3), (2010)132-138.
  • Duranda M, Langevin D. Physicochemical approach to the theory of foam drainage. The European Physical Journal E 7(1), (2002) 35-44.
  • Fan E. Extended tanh-function method and its applications to nonlinear equations. physic letter A 277(4-5), (2000) 212-218.
  • Hone ANW. Painleve tests, singularity structure and integrability. Lect Notes Physics . (2009) . 767 245-277.
  • Jafari H, Kadkhoda N, Biswas A. The -expansion method for solutions of evolution equations from isothermal magnetostatic atmospheres. Journal of King Saud University – Science [In Press]. Kudryashov NA. On types of nonlinear integrable equations with exact solutions. physic letter A 155(4–5), (1991) 269-275.
  • Kudryashov NA. Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos, Solitons & Fractals 24(5), (2005) 1217-1231.
  • Kudryashov NALoguinova NB. Extended simplest equation method for nonlinear differential equations. Applied Mathematics and Computation 205 (1),(2008) 396-402.
  • Ostrovsky LANonlinear internal waves in a rotating ocean. Okeanologiya 1978;18:181-91 [in Russian] (Engl transl: Oceanology 18 119- 125) (1978).
  • Salehpour1 E, Jafari H, Kadkhoda N. Application of -expansion method to nonlinear Lienard equation. Indian Jour of Science and Technology 5(4), (2012) 2554-2556.
  • Wazwaz A.M. New solutions of distinct physical structures to highdimensional nonlinear evolution equations, Applied Mathematics and Computation 196(1) (2008) 363–370.
  • Wazwaz A.M. The (2+1) and (3+1)-Dimensional CBS Equations: Multiple Soliton Solutions and Multiple Singular Soliton Solutions, Zeitschrift fur Naturforschung A 65a, (2010) 173–181.
  • Wazwaz A.M Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations, Applied Mathematics and Computation 203(2), (2008) 592–597.
  • Wazwaz A.M. The tanh-coth method for solitons and kink solutions fornon-linear parabolic equations, Applied Mathematics and Computation 188(2), (2007) 1467-1475.
  • Wazwaz A.M. A sine-cosine method for handling nonlinear wave equations. Mathematical and Computer Modelling 40(5-6) ,(2004) 499- 50
There are 14 citations in total.

Details

Journal Section Articles
Authors

Hossein Jafari This is me

Nematollah Kadkhoda This is me

Publication Date August 1, 2014
Published in Issue Year 2014 Volume: 2 Issue: 2

Cite

APA Jafari, H., & Kadkhoda, N. (2014). Application of simplest equation method to the (2+1)-dimensional nonlinear evolution equations. New Trends in Mathematical Sciences, 2(2), 64-68.
AMA Jafari H, Kadkhoda N. Application of simplest equation method to the (2+1)-dimensional nonlinear evolution equations. New Trends in Mathematical Sciences. August 2014;2(2):64-68.
Chicago Jafari, Hossein, and Nematollah Kadkhoda. “Application of Simplest Equation Method to the (2+1)-Dimensional Nonlinear Evolution Equations”. New Trends in Mathematical Sciences 2, no. 2 (August 2014): 64-68.
EndNote Jafari H, Kadkhoda N (August 1, 2014) Application of simplest equation method to the (2+1)-dimensional nonlinear evolution equations. New Trends in Mathematical Sciences 2 2 64–68.
IEEE H. Jafari and N. Kadkhoda, “Application of simplest equation method to the (2+1)-dimensional nonlinear evolution equations”, New Trends in Mathematical Sciences, vol. 2, no. 2, pp. 64–68, 2014.
ISNAD Jafari, Hossein - Kadkhoda, Nematollah. “Application of Simplest Equation Method to the (2+1)-Dimensional Nonlinear Evolution Equations”. New Trends in Mathematical Sciences 2/2 (August 2014), 64-68.
JAMA Jafari H, Kadkhoda N. Application of simplest equation method to the (2+1)-dimensional nonlinear evolution equations. New Trends in Mathematical Sciences. 2014;2:64–68.
MLA Jafari, Hossein and Nematollah Kadkhoda. “Application of Simplest Equation Method to the (2+1)-Dimensional Nonlinear Evolution Equations”. New Trends in Mathematical Sciences, vol. 2, no. 2, 2014, pp. 64-68.
Vancouver Jafari H, Kadkhoda N. Application of simplest equation method to the (2+1)-dimensional nonlinear evolution equations. New Trends in Mathematical Sciences. 2014;2(2):64-8.