Existence of traveling-wave solutions to Boussinesq systems
Existence of traveling-wave solutions to Boussinesq systems
复制标题
Boussinesq 系统行波解的存在性
DOI：
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发表时间：
2011
影响因子：
1.4
通讯作者：
Shu
中科院分区：
文献类型：
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作者：
Min Chen;Nghiem V. Nguyen;Shu
本文建立了Boussinesq系统ηt + ux + (ηu)x + auxxx−bηxxt = 0, ut + ηx + uux + cηxxx−duxxt = 0行波解的存在性。我们证明了所有a < 0, c < 0, b = d的系统都具有小传播速度的行波解。这个结果补充了我们之前在一个有限的系统族上的工作，在这个系统族中，行波解的存在性和稳定性都是在大表面张力存在的情况下建立的，即当a+ b+ c+ d < 0时。
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.