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- W1041662008 abstract "The purpose of this paper is to provide a mathematical proof of the existence of smooth solitary travelling waves for a coupled system of Korteweg–de Vries type equations {ut+uxxx+(upvp+1)x=0,vt+rvx+vxxx+(up+1vp)x=0, where u=u(x,t),v=v(x,t) are real-valued functions and r,x,t∈R. We follow a variational approach by characterizing travelling waves as minimizers of some functional under suitable constraints. Using the modern methods in the calculus of variations (the concentration-compactness principle of P. L. Lions), we prove that any minimizing sequence for the variational problem converges strongly, after an appropriate translation, to a minimizer." @default.
- W1041662008 created "2016-06-24" @default.
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- W1041662008 date "2015-11-01" @default.
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- W1041662008 title "Existence of travelling-wave solutions to a coupled system of Korteweg–de Vries equations" @default.
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- W1041662008 doi "https://doi.org/10.1016/j.na.2015.07.004" @default.
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