Comparison of solutions of Boussinesq systems
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چکیده
We compare the solution of the generalized Boussinesq systems, for various values of a,b,c,d, ηt + ux + ε((ηu)x + auxxx − bηxxt) = 0 ut + ηx + ε(uux + cηxxx − duxxt) = 0. These systems describe the two-way propagation of small amplitude long waves in shallow water. We prove, using an energy method introduced by Bona, Pritchard and Scott [7], that respective solutions of Boussinesq systems, starting from the same initial datum, remain close on a time interval inversely proportional to the wave amplitude.
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تاریخ انتشار 2017