We study a stochastic Schrödinger equation with quadratic nonlinearity and space-time fractional perturbation, in space dimension d ≤ 3 <mml:annotation encodin...

The main scope of this paper is to examine the smoke ring (or vortex filament) equation which can be viewed as a dynamical system on space curve in E³. differential geometric properties soliton surface accociated with Nonlinear Schrödinger (NLS) equation, called NLS or Hasimoto surface, are investigated by using Darboux frame. Moreover, Gaussian and mean curvature found terms curvatures k_{n}, ...

The Schrödinger-Newton equation has gained attention in the recent past as a nonlinear modification of the Schrödinger equation due to a gravitational self-interaction. Such a modification is expected from a fundamentally semi-classical theory of gravity and can, therefore, be considered a test case for the necessity of the quantisation of the gravitational field. Here we provide a thorough stu...

This paper is concerned with interacting wave packet dynamics for long waves. The Kortweg-de Vries equation is the most well-known model for weakly nonlinear long waves. Although the dynamics of a single wave packet in this model is governed by the defocusing nonlinear Schrödinger equation, implying that a plane wave is modulationally stable, the dynamics of two interacting wave packets is gove...