## Travelling wave solutions of generalized forms of Burgers, Burgers-KdV and Burgers-Huxley equations.(English)Zbl 1078.35109

Summary: Exact travelling wave solutions of generalized forms of Burgers, Burgers-KdV and Burgers-Huxley equations are obtained. The analysis rests mainly on the standard tanh method. The work emphasizes the need for a transformation formula for the case where the parameter $$M$$ is non-integer.

### MSC:

 35Q53 KdV equations (Korteweg-de Vries equations) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 35C05 Solutions to PDEs in closed form 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems

MACSYMA
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### References:

 [1] Wang, X.Y., Exact and explicit solitary wave solutions for the generalized Fisher equation, Phys. lett. A, 131, 4/5, 277-279, (1988) [2] Jeffrey, A.; Mohamad, M.N.B., Exact solutions to the KdV-burgers’ equation, Wave motion, 14, 369-375, (1991) · Zbl 0833.35124 [3] Wadati, M., The exact solution of the modified Korteweg-de Vries equation, J. phys. soc. jpn., 32, 1681-1687, (1972) [4] Kivshar, Y.S.; Pelinovsky, D.E., Self-focusing and transverse instabilities of solitary waves, Phys. rep., 331, 117-195, (2000) [5] Hereman, W.; Takaoka, M., Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA, J. phys. A, 23, 4805-4822, (1990) · Zbl 0719.35085 [6] Malfliet, W., Solitary wave solutions of nonlinear wave equations, Am. J. phys., 60, 7, 650-654, (1992) · Zbl 1219.35246 [7] Malfliet, W., The tanh method: I. exact solutions of nonlinear evolution and wave equations, Phys. scr., 54, 563-568, (1996) · Zbl 0942.35034 [8] Malfliet, W., The tanh method: II. perturbation technique for conservative systems, Phys. scr., 54, 569-575, (1996) · Zbl 0942.35035 [9] Wazwaz, A.M., The tanh method for travelling wave solutions of nonlinear equations, Appl. math. comput., 154, 3, 713-723, (2004) · Zbl 1054.65106 [10] Wazwaz, A.M., Partial differential equations: methods and applications, (2002), Balkema Publishers The Netherlands · Zbl 0997.35083 [11] Wazwaz, A.M., New solitary-wave special solutions with compact support for the nonlinear dispersive K(m,n) equations, Chaos solitons fract., 13, 2, 321-330, (2002) · Zbl 1028.35131 [12] Wazwaz, A.M., Exact specific solutions with solitary patterns for the nonlinear dispersive K(m,n) equations, Chaos solitons fract., 13, 1, 161-170, (2001) · Zbl 1027.35115 [13] Wazwaz, A.M., General compactons solutions for the focusing branch of the nonlinear dispersive K(n,n) equations in higher dimensional spaces, Appl. math. comput., 133, 2/3, 213-227, (2002) · Zbl 1027.35117 [14] Wazwaz, A.M., General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive K(n,n) equations in higher dimensional spaces, Appl. math. comput., 133, 2/3, 229-244, (2002) · Zbl 1027.35118 [15] Wazwaz, A.M., Compactons and solitary patterns structures for variants of the KdV and the KP equations, Appl. math. comput., 139, 1, 37-54, (2003) · Zbl 1029.35200 [16] Wazwaz, A.M., A construction of compact and noncompact solutions of nonlinear dispersive equations of even order, Appl. math. comput., 135, 2-3, 411-424, (2003) · Zbl 1027.35121 [17] Wazwaz, A.M., Compactons in a class of nonlinear dispersive equations, Math. comput. modell., 37, 3/4, 333-341, (2003) · Zbl 1044.35078 [18] Wazwaz, A.M., Distinct variants of the KdV equation with compact and noncompact structures, Appl. math. comput., 150, 365-377, (2004) · Zbl 1039.35110 [19] Wazwaz, A.M., Variants of the generalized KdV equation with compact and noncompact structures, Comput. math. appl., 47, 583-591, (2004) · Zbl 1062.35120 [20] Wazwaz, A.M., New compactons, solitons and periodic solutions for nonlinear variants of the KdV and the KP equations, Chaos solitons fract., 22, 249-260, (2004) · Zbl 1062.35121
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