Exact Three-wave Solutions for High Nonlinear Form of Benjamin-Bona-Mahony-Burgers Equations
By means of the idea of three-wave method, we obtain some analytic solutions for high nonlinear form of Benjamin-Bona- Mahony-Burgers (shortly BBMB) equations in its bilinear form.
[1] M. Mei, Large-time behavior of solution for generalized Benjamin-Bona-
Mahony-Burgers equations, Nonlinear Analysis, 33 (1998) 699-714.
[2] K. Al-Khaled, S. Momani, A. Alawneh, Approximate wave solutions
for generalized Benjamin-Bona-Mahony-Burgers equations, Appl. Math.
Comput., 171 (2005) 281-292.
[3] H. Tari, D.D. Ganji, Approximate explicit solutions of nonlinear BBMB
equations by Hes methods and comparison with the exact solution, Phys.
Lett. A, 367 (2007) 95-101.
[4] A. Fakhari, Ganji Domairry, Ebrahimpour, Approximate explicit solutions
of nonlinear BBMB equations by homotopy analysis method and comparison
with the exact solution, Phys. Lett. A, 368 (2007) 64-68.
[5] H. Yin, H.-J. Zhao, J.-S. Kim, Convergence rates of solutions toward
boundary layer solutions for generalized Benjamin-Bona-Mahony-
Burgers equations in the half-space, J. Differential Equations, 245 (2008)
3144-3216.
[6] Z.Z. Ganji, D.D. Ganji, H. Bararnia, Approximate general and explicit
solutions of nonlinear BBMB equations by Exp-Function method, Appl.
Math.l Modelling, 33 (2009) 1836-1841.
[7] M. Kazeminia, P. Tolou, J. Mahmoudi, I. Khatami, I. Khatami, Solitary
and Periodic Solutions of BBMB Equation via Exp-Function Method,
Adv. Studies Theor. Phys., 3(12) (2009) 461-471.
[8] H. Yin., J. Hu, Exponential decay rate of solutions toward traveling waves
for the Cauchy problem of generalized Benjamin-Bona-Mahony-Burgers
equations, Nonlinear Analysis, 73 (2010) 1729-1738.
[9] Z.-D. Dai, S.-Q. Lin. D.-L. Li, G. Mu, The three-wave method for
nonlinear evalution equations, Nonl. Sci. Lett. A, 1(1) (2010) 77-82.
[10] C.-J. Wang, Z.-D. Dai, L. Liang, Exact three-wave solution for higher
dimensional KDV-type equation, Appl. Math. Comput., 216 (2010) 501-
505.
[1] M. Mei, Large-time behavior of solution for generalized Benjamin-Bona-
Mahony-Burgers equations, Nonlinear Analysis, 33 (1998) 699-714.
[2] K. Al-Khaled, S. Momani, A. Alawneh, Approximate wave solutions
for generalized Benjamin-Bona-Mahony-Burgers equations, Appl. Math.
Comput., 171 (2005) 281-292.
[3] H. Tari, D.D. Ganji, Approximate explicit solutions of nonlinear BBMB
equations by Hes methods and comparison with the exact solution, Phys.
Lett. A, 367 (2007) 95-101.
[4] A. Fakhari, Ganji Domairry, Ebrahimpour, Approximate explicit solutions
of nonlinear BBMB equations by homotopy analysis method and comparison
with the exact solution, Phys. Lett. A, 368 (2007) 64-68.
[5] H. Yin, H.-J. Zhao, J.-S. Kim, Convergence rates of solutions toward
boundary layer solutions for generalized Benjamin-Bona-Mahony-
Burgers equations in the half-space, J. Differential Equations, 245 (2008)
3144-3216.
[6] Z.Z. Ganji, D.D. Ganji, H. Bararnia, Approximate general and explicit
solutions of nonlinear BBMB equations by Exp-Function method, Appl.
Math.l Modelling, 33 (2009) 1836-1841.
[7] M. Kazeminia, P. Tolou, J. Mahmoudi, I. Khatami, I. Khatami, Solitary
and Periodic Solutions of BBMB Equation via Exp-Function Method,
Adv. Studies Theor. Phys., 3(12) (2009) 461-471.
[8] H. Yin., J. Hu, Exponential decay rate of solutions toward traveling waves
for the Cauchy problem of generalized Benjamin-Bona-Mahony-Burgers
equations, Nonlinear Analysis, 73 (2010) 1729-1738.
[9] Z.-D. Dai, S.-Q. Lin. D.-L. Li, G. Mu, The three-wave method for
nonlinear evalution equations, Nonl. Sci. Lett. A, 1(1) (2010) 77-82.
[10] C.-J. Wang, Z.-D. Dai, L. Liang, Exact three-wave solution for higher
dimensional KDV-type equation, Appl. Math. Comput., 216 (2010) 501-
505.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57726", author = "Mohammad Taghi Darvishi and Maliheh Najafi and Mohammad Najafi", title = "Exact Three-wave Solutions for High Nonlinear Form of Benjamin-Bona-Mahony-Burgers Equations", abstract = "By means of the idea of three-wave method, we obtain some analytic solutions for high nonlinear form of Benjamin-Bona- Mahony-Burgers (shortly BBMB) equations in its bilinear form.
", keywords = "Benjamin-Bona-Mahony-Burgers equations, Hirota's bilinear form, three-wave method.", volume = "4", number = "1", pages = "87-5", }
