科研之友
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摘要
In this pager, we study the elliptic singular wave solutions of the equation u(t) + 2ku(x) - u(xxt) + u(2)u(x) - uu(xxx) = 0 which has been investigated in some literatures. Firstly, for given wave speeds c(1) = 1/2 (1 + root 1 - 8k) or c(2) = 1/2 (1 - root 1 - 8k), we show that there exist four types of elliptic singular wave solutions, two types of elliptic sine singular wave solutions and two types of elliptic cosine singular wave solutions. Secondly, we confirm that their limits are four types of other solutions, hyperbolic smooth solitary wave solutions, hyperbolic singular wave solutions, fractional singular wave solution and trigonometric singular wave solutions. Our works extend some previous results.
