1Department of Mathematics, Jaypee University of Information Technology, Waknaghat, P.O. Dumehar Bani, Kandaghat, Distt. Solan, Pin-173215 (H.P.), India
2School of Mathematics and Computer Applications. Thapar University, Patiala-147004 (Punjab), India
3School of Mathematics and Computer Applications. Thapar University, Patiala-147004 (Punjab), India
4Department of Applied Sciences, Ferozepur College of Engineering and Technology, Ferozshah
*Author for corresponding: E-mail: sachin1jan@yahoo.com, rajeshgupta@thapar.edu
** E-mail: rajeshateli@rediffmail.com, sachin1jan@yahoo.com
*** E-mail: karan_jeet@yahoo.com
**** E-mail: anupma2512@yahoo.co.in
The b-family equation ut – uxxt + (b + 1) uux = buxuxx + uuxxx is introduced by D.D. Holm and M.F. Struley, which describes the balance between the convection and the stretching for small viscosity in the dynamics of 1D non-linear waves in fluids. In this paper we first performed direct method introduced by Clarkson and Kruksal (1989) for symmetries of the modified b-family equation ut – u + (b + 1) u2ux = buxuxx + uuxxx. Second using symmetries of the equation, similarity reductions are obtained and we show some exact solutions.
Modified b-family equation, Direct method, Symmetry reductions, Exact solutions
