Abstract We analyze dynamical properties of the logarithmic Schrödinger equation under a quadratic potential. The sign nonlinearity is such that it known in absence external potential, every solution dispersive, with universal asymptotic profile. introduction harmonic potential generates solitary waves, corresponding to generalized Gaussons. prove they are orbitally stable, using an inequality ...

Abstract: The non-zero unique integer solutions to the quadratic Diophantine equation with three unknowns 2 x  14 xy y  z are examined. We derive integral in four different patterns. A few intriguing relationships between answers and a polygonal integers shown

In this paper, we study a quadratic nonlinear equation from the fractional point of view. An explicit solution is given in terms Lambert special function. A new phenomenon appears involving collapsing and blow-up derivative. The representation reveals non-elementary nature solution.

in this paper, we introduce an efficient method for solving the quadratic riccati differential equation. in this technique, combination of laplace transform and new homotopy perturbation methods (ltnhpm) are considered as an algorithm to the exact solution of the nonlinear riccati equation. unlike the previous approach for this problem, so-called nhpm, the present method, does not need the init...

We are considering the application of the Augmented Lagrangian algorithms with quadratic penalty, to convex problems of quadratic programming. The problems of quadratic programming are composites of quadratic objective function and linear constraints. This important class of problems will be generated through the algorithm of sequential quadratic programming, where at each iteration the quadrat...