Obliquely interacting solitary waves

摘要: Nonlinear oblique interactions between two slightly dispersive gravity waves (in particular, solitary waves) of dimensionless amplitudes α1 and α2 (relative to depth) relative inclination 2ϕ (between wave normals) are classified as weak if sin2ϕ α1,2 or strong ϕ2 = O(α1,2). Weak permit superposition the individual solutions Korteweg-de Vries equation in first approximation; interaction term, which is O(α1α2), then determined from these basic solutions.Strong intrinsically nonlinear. It shown that phase-conserving (the sum phases incoming equal outgoing |α2-α1 > (2ϕ)2 but not |α2-α1| (e.g. reflexion problem, for interacting images α1). also singular, sense regular with sech2 profiles yield singular - csch2 profiles, if \[ \psi_{-}< |\psi| < \psi_{+},\quad{\rm where}\quad\psi_{\pm}={\textstyle\frac{1}{2}}\left|(3\alpha_2)^{\frac{1}{2}}\pm(3\alpha_1)^{\frac{1}{2}}\right|. \]Regular appear be impossible within this regime, its end points, |ϕ| ϕ±, associated resonant interactions.