Existence of Traveling-wave Solutions to Boussinesq Systems
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چکیده
In this manuscript, the existence of traveling-wave solutions to Boussinesq systems ηt + ux + (ηu)x + auxxx − bηxxt = 0, ut + ηx + uux + cηxxx − duxxt = 0, is established. We prove that all the systems with a < 0, c < 0 and b = d exhibit traveling-wave solutions with small propagation speeds. The result complements our earlier work [6] on a restricted family of the systems where both existence and stability of traveling-wave solutions were established in the presence of large surface tension, namely when a+ b+ c+ d < 0.
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تاریخ انتشار 2011