Solitary wave solutions of the one-dimensional Boussinesq equations

Abstract

In this paper we derive an analytical solution of the one-dimensional Boussinesq equations, in the case of waves relatively long, with small amplitudes, in water of varying depth. To derive the analytical solution we first assume that the solution of the model has a prescribed wave form, and then we obtain the wave velocity, the wave number and the wave amplitude. Finally a specific application for some realistic values of wave parameters is given and a graphical presentation of the results is provided.

Soliton solutions for (2+1) and (3+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony model equations and their applications

“…The solitary wave Ansatz method [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] have been adopted to present the solutions of (2+1) and (3+1)-Dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equations, are respectively defined by…”