Dynamics of Shallow Water Waves with Various Boussinesq Equations
H. Kumara, A. Malik b, M. Singh Gautam c and F. Chand d
aDepartment of Physics, Dr. B.R. Ambedkar Institute of Technology, Port Blair-744103, India
bDepartment of Physics, Chaudhary Bansi Lal University, Bhiwani-127021, India
cDepartment of Physics, Indus Degree College, Jind-126102, India
dDepartment of Physics, Kurukshetra University, Kurukshetra-136119, India
Received: September 18, 2016; In final form: January 16, 2017
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Attempt has been made to construct the solitary waves and shock wave solutions or domain walls (in higher dimension) for various Boussinesq equations. The method of undetermined coefficients have been used to explore the exact analytical solitary waves and shock wave solutions in terms of bell-shaped sechp function and kink-shaped tanhp function for the considered equations. The Boussinesq equation in the (1+1)-dimensional, the (2+1)-dimensional and the (3+1)-dimensional equations are studied and the parametric constraint conditions and uniqueness in view of both solitary waves and shock wave solutions are determined. Such solutions can be valuable and desirable for explaining some nonlinear physical phenomena in nonlinear science described by the Boussinesq equations. The effect of the varying parameters on the development of solitary waves and shock wave solutions have been demonstrated by direct numerical simulation technique.

DOI: 10.12693/APhysPolA.131.275
PACS numbers/topics: Solitons, exact solutions, Boussinesq equation