The possibility of finite-time, dispersive blow up for nonlinear equations of Schrödinger type is revisited. This mathematical phenomena is one of the possible explanations for oceanic and optical rogue waves. In dimension one, the possibility of dispersive blow up for nonlinear Schrödinger equations already appears in [9]. In the present work, the existing results are extended in several ways....

In this paper, we provide a class of surfaces called ϵ-isothermic surface in the pseudo-Euclidean 3-space and introduce pseudo-Calapso equation. We prove that for each surface, can associate two solutions to particular, Calapso, Zoomeron Davey-Stewartson III equations. sequence, classify Dupin having distinct principal curvatures explicit coordinates such surfaces. As application theory, obtain...

The existence of standing waves for a generalized Davey–Stewartson (GDS) system was shown in Eden and Erbay [8] using an unconstrainted minimization problem. Here, we consider the same problem but relax the condition on the parameters to χ+b < 0 or χ + b m1 < 0. Our approach, in the spirit of Berestycki, Gallouët and Kavian [3] and Cipolatti [6], is to use a constrained minimization problem and...