The extended tanh method and its applications for solving nonlinear physical models

The extended tanh method with a computerized symbolic computation is used for constructing the travelling wave solutions of coupled nonlinear equations arising in physics. The obtained solutions include solitons, kinks and plane periodic solutions. The applied method will be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics.

[1]  S. A. El-Wakil,et al.  Modified extended tanh-function method and its applications to nonlinear equations , 2005, Appl. Math. Comput..

[2]  Abdul-Majid Wazwaz,et al.  The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations , 2005, Appl. Math. Comput..

[3]  W. Malfliet.  Solitary wave solutions of nonlinear wave equations , 1992 .

[4]  Abdul-Majid Wazwaz,et al.  The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation , 2005, Appl. Math. Comput..

[5]  Qi Wang,et al.  Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1 + 1)-dimensional dispersive long wave equation , 2005 .

[6]  A. A. Soliman,et al.  The modified extended tanh-function method for solving Burgers-type equations , 2006 .

[7]  S. A. El-Wakil,et al.  Modified extended tanh-function method for solving nonlinear partial differential equations , 2002 .

[8]  M. A. Abdou,et al.  The extended homogeneous balance method and its applications for a class of nonlinear evolution equations , 2007 .

[9]  M. A. Abdou,et al.  New exact travelling wave solutions of two nonlinear physical models , 2008 .

[10]  M. A. Abdou,et al.  Modified extended tanh-function method for solving nonlinear partial differential equations , 2007 .

[11]  Abdul-Majid Wazwaz,et al.  The tan h method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations , 2005 .

[12]  A. A. Soliman,et al.  Modified extended tanh-function method and its application on nonlinear physical equations , 2006 .

[13]  Abdul-Majid Wazwaz,et al.  The extended tanh method for abundant solitary wave solutions of nonlinear wave equations , 2007, Appl. Math. Comput..

[14]  M. A. Abdou,et al.  New solitons and periodic wave solutions for nonlinear evolution equations , 2006 .

[15]  M. A. Abdou,et al.  Construction of periodic and solitary wave solutions by the extended Jacobi elliptic function expansion method , 2007 .

[16]  Abdul-Majid Wazwaz,et al.  The tanh method for traveling wave solutions of nonlinear equations , 2004, Appl. Math. Comput..

[17]  Abdul-Majid Wazwaz,et al.  The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations , 2007, Appl. Math. Comput..

[18]  A. Wazwaz.  THE TANH AND THE SINE–COSINE METHODS FOR A RELIABLE TREATMENT OF THE MODIFIED EQUAL WIDTH EQUATION AND ITS VARIANTS , 2006 .

[19]  Abdul-Majid Wazwaz,et al.  The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations , 2005, Appl. Math. Comput..

[20]  M. A. Abdou,et al.  New exact travelling wave solutions using modified extended tanh-function method , 2007 .

[21]  Abdul-Majid Wazwaz,et al.  Nonlinear variants of the improved Boussinesq equation with compact and noncompact structures , 2005 .