Shock Waves and Other Solutions to the Benjamin-Bona-Mahoney-Burgers Equation with Dual Power-Law Nonlinearity
G.-W. Wang a, T.-Z. Xu a, R. Abazari b, Z. Jovanoski c and A. Biswasd,e
aSchool of Mathematics and Statistics, Beijing Institute of Technology, Beijing-100081, People's Republic of China
bYoung Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran
cApplied and Industrial Mathematics Research Group, School of Physical, Environmental and Mathematical Sciences, UNSW Canberra, ACT 2600, Australia
dDepartment of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA
eDepartment of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah-21589, Saudi Arabia
Received: April 22, 2014
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We study the hybrid Benjamin-Bona-Mahoney-Burgers equation with dual power-law nonlinearity. Three different techniques - the ansatz method, Lie-symmetry analysis and the (G'/G)-expansion method - are used to find shock wave solutions. Several constraint conditions naturally emerge that guarantee the existence of shock waves. We discuss the nature of the solutions generated by the different methods.

DOI: 10.12693/APhysPolA.126.1221
PACS numbers: 02.30.Ik; 02.30.Jr; 02.20.Qs