Department of Applied Physics, Hanyang University, Ansan, Kyunggi-Do 426-791, South Korea_c

摘要

A general theory for the existence of solitary structure at M = Mc has been discussed, where Mc is the lower bound of the Mach number M, i.e., solitary structures start to exist for M >M c. Three important results have been proved to confirm the existence of solitary structure at M = M c. If V(?)(= V(M,?)) denotes the Sagdeev potential with ? being the perturbed field or perturbed dependent variable associated with a specific problem, V(M,?) is well defined as a real number for all M ∈ M and ?∈. ψ 0, and V(M, 0) = V′(M, ?) = V′′(M c, 0) = 0, V′′′M c, 0) 0 (V′′′(M c, 0) > 0),?V/?M < 0 for all M(∈ M)> 0 and ?(∈ φ 0) > 0 (?(∈ φ 0) < 0), where ′ = ?/?? ', the main analytical results for the existence of solitary wave or double layer solution of the energy integral at M = M c are as follows. Result 1: If there exists at least one value M 0 of M such that the system supports positive (negative) potential solitary waves for all Mc < M