Extend Three-wave Method for the (3+1)-Dimensional Soliton Equation
In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota-s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented.
[1] A.M. Wazwaz,The tanh method: solitons and periodic solutions for the
Dodd-Bullough-Tzikhailov and the Tzitzeica-Dodd-Bullough equations,
Chaos, Solitons and Fractals 25 (2005)55-63.
[2] Z. Xiqiang, W. Limin, S. Weijun, The repeated homogeneous balance
method and its applications to nonlinear partial differential equations,
Chaos, Solitons and Fractals, 28(2) (2006) 448-453.
[3] S.J. Liao, Beyond Perturbation: Introduction to the homotopy analysis
method, Chapman & Hall/CRC Press, Boca Raton, 2003.
[4] S.J. Liao, On the homotopy analysis method for nonlinear problems, Appl.
Math. Comput., 147 (2006) 499-513.
[5] S.J. Liao, A general approach to get series solution of nonsimilarity
boundary-layer flows, Commun. Nonlinear Sci. Numer. Simul.,
14(5)(2009) 2144-2159.
[6] M.T. Darvishi, F. Khani, A series solution of the foam drainage equation,
Comput. Math. Appl., 58 (2009) 360-368.
[7] A. Aziz, F. Khani, M.T. Darvishi, Homotopy analysis method for variable
thermal conductivity heat flux gage with edge contact resistance,
Zeitschrift fuer Naturforschung A, 65a(10)(2010) 771-776.
[8] F. Khani, M.T. Darvishi, R.S.R. Gorla, Analytical investigation for cooling
turbine disks with a non-Newtonian viscoelastic fluid, Comput. Math.
Appl., 61(7)(2011) 1728-1738.
[9] E. Fan, Z. Jian, Applications of the Jacobi elliptic function method to
special-type nonlinear equations, Phys. Lett. A, 305(6) (2002) 383-392.
[10] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, Exact three-wave
solutions for high nonlinear form of Benjamin-Bona-Mahony-Burgers
equations, International Journal of Mathematical and Computer Sciences,
6(3)(2010) 127-131.
[11] M.T. Darvishi, M. Najafi, Some exact solutions of the (2+1)-dimensional
breaking soliton equation using the three-wave method, International
Journal of Computational and Mathematical Sciences, 6(1)(2012)13-16.
[12] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, New exact solutions
for the (3+1)-dimensional breaking soliton equation, International Journal
of Information and Mathematical Sciences, 6(2)(2010) 134-137.
[13] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, New application
of EHTA for the generalized (2+1)-dimensional nonlinear evolution
equations, International Journal of Mathematical and Computer Sciences,
6(3)(2010) 132-138.
[14] M.T. Darvishi, M. Najafi, A modification of extended homoclinic test
approach to solve the (3+1)-dimensional potential-YTSF equation, Chin.
Phys. Lett., 28(4)(2011) 040202.
[15] M.T. Darvishi, M. Najafi, Some complexiton type solutions of the (3+1)-
dimensional Jimbo-Miwa equation, International Journal of Computational
and Mathematical Sciences, 6(1)(2012) 25-27.
[16] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, Traveling wave
solutions for the (3+1)-dimensional breaking soliton equation by (G
G )-
expansion method and modified F-expansion method, International Journal
of Computational and Mathematical Sciences, 6(2)(2012) 64-69.
[17] J.H. He, M.A. Abdou,New periodic solutions for nonlinear evolution
equations using Exp-function method, Chaos, Solitons and Fractals, 34
(2007) 1421-1429.
[18] F. Khani, S. Hamedi-Nezhad, M.T. Darvishi, S.-W. Ryu, New solitary
wave and periodic solutions of the foam drainage equation using the Expfunction
method, Nonlin. Anal.: Real World Appl., 10 (2009) 1904-1911.
[19] B.-C. Shin, M.T. Darvishi, A. Barati, Some exact and new solutions
of the Nizhnik-Novikov-Vesselov equation using the Exp-function method,
Comput. Math. Appl., 58(11/12) (2009) 2147-2151.
[20] F. Khani, M.T. Darvishi, A. Farmani, L. Kavitha, New exact solutions
of coupled (2+1)-dimensional nonlinear system of Schr¨odinger equations,
ANZIAM Journal, 52 (2010) 110-121.
[21] X.H. Wu, J.H. He, Exp-function method and its application to nonlinear
equations, Chaos, Solitons and Fractals, 38(3)(2008) 903-910.
[22] 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.
[23] 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.
[24] J.-O. WU, X.-G. GENG, Grammian Determinant Solution and Pfaffianization
for a (3+1)-Dimensional Soliton Equation, Commun. Theor.
Phys. (Beijing, China) 52 (2009) 791-794.
[1] A.M. Wazwaz,The tanh method: solitons and periodic solutions for the
Dodd-Bullough-Tzikhailov and the Tzitzeica-Dodd-Bullough equations,
Chaos, Solitons and Fractals 25 (2005)55-63.
[2] Z. Xiqiang, W. Limin, S. Weijun, The repeated homogeneous balance
method and its applications to nonlinear partial differential equations,
Chaos, Solitons and Fractals, 28(2) (2006) 448-453.
[3] S.J. Liao, Beyond Perturbation: Introduction to the homotopy analysis
method, Chapman & Hall/CRC Press, Boca Raton, 2003.
[4] S.J. Liao, On the homotopy analysis method for nonlinear problems, Appl.
Math. Comput., 147 (2006) 499-513.
[5] S.J. Liao, A general approach to get series solution of nonsimilarity
boundary-layer flows, Commun. Nonlinear Sci. Numer. Simul.,
14(5)(2009) 2144-2159.
[6] M.T. Darvishi, F. Khani, A series solution of the foam drainage equation,
Comput. Math. Appl., 58 (2009) 360-368.
[7] A. Aziz, F. Khani, M.T. Darvishi, Homotopy analysis method for variable
thermal conductivity heat flux gage with edge contact resistance,
Zeitschrift fuer Naturforschung A, 65a(10)(2010) 771-776.
[8] F. Khani, M.T. Darvishi, R.S.R. Gorla, Analytical investigation for cooling
turbine disks with a non-Newtonian viscoelastic fluid, Comput. Math.
Appl., 61(7)(2011) 1728-1738.
[9] E. Fan, Z. Jian, Applications of the Jacobi elliptic function method to
special-type nonlinear equations, Phys. Lett. A, 305(6) (2002) 383-392.
[10] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, Exact three-wave
solutions for high nonlinear form of Benjamin-Bona-Mahony-Burgers
equations, International Journal of Mathematical and Computer Sciences,
6(3)(2010) 127-131.
[11] M.T. Darvishi, M. Najafi, Some exact solutions of the (2+1)-dimensional
breaking soliton equation using the three-wave method, International
Journal of Computational and Mathematical Sciences, 6(1)(2012)13-16.
[12] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, New exact solutions
for the (3+1)-dimensional breaking soliton equation, International Journal
of Information and Mathematical Sciences, 6(2)(2010) 134-137.
[13] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, New application
of EHTA for the generalized (2+1)-dimensional nonlinear evolution
equations, International Journal of Mathematical and Computer Sciences,
6(3)(2010) 132-138.
[14] M.T. Darvishi, M. Najafi, A modification of extended homoclinic test
approach to solve the (3+1)-dimensional potential-YTSF equation, Chin.
Phys. Lett., 28(4)(2011) 040202.
[15] M.T. Darvishi, M. Najafi, Some complexiton type solutions of the (3+1)-
dimensional Jimbo-Miwa equation, International Journal of Computational
and Mathematical Sciences, 6(1)(2012) 25-27.
[16] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, Traveling wave
solutions for the (3+1)-dimensional breaking soliton equation by (G
G )-
expansion method and modified F-expansion method, International Journal
of Computational and Mathematical Sciences, 6(2)(2012) 64-69.
[17] J.H. He, M.A. Abdou,New periodic solutions for nonlinear evolution
equations using Exp-function method, Chaos, Solitons and Fractals, 34
(2007) 1421-1429.
[18] F. Khani, S. Hamedi-Nezhad, M.T. Darvishi, S.-W. Ryu, New solitary
wave and periodic solutions of the foam drainage equation using the Expfunction
method, Nonlin. Anal.: Real World Appl., 10 (2009) 1904-1911.
[19] B.-C. Shin, M.T. Darvishi, A. Barati, Some exact and new solutions
of the Nizhnik-Novikov-Vesselov equation using the Exp-function method,
Comput. Math. Appl., 58(11/12) (2009) 2147-2151.
[20] F. Khani, M.T. Darvishi, A. Farmani, L. Kavitha, New exact solutions
of coupled (2+1)-dimensional nonlinear system of Schr¨odinger equations,
ANZIAM Journal, 52 (2010) 110-121.
[21] X.H. Wu, J.H. He, Exp-function method and its application to nonlinear
equations, Chaos, Solitons and Fractals, 38(3)(2008) 903-910.
[22] 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.
[23] 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.
[24] J.-O. WU, X.-G. GENG, Grammian Determinant Solution and Pfaffianization
for a (3+1)-Dimensional Soliton Equation, Commun. Theor.
Phys. (Beijing, China) 52 (2009) 791-794.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:58270", author = "Somayeh Arbabi Mohammad-Abadi and Maliheh Najafi", title = "Extend Three-wave Method for the (3+1)-Dimensional Soliton Equation", abstract = "In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota-s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented.
", keywords = "Three-wave method, (3+1)-dimensional Soliton equation, Hirota's bilinear form.", volume = "5", number = "8", pages = "1329-4", }
