In this work, we will first review the Quantum Mechanics theory to derive the main equations. Next, we will analyze these equations by Functional Analysis methods to find conditions for existence, uniqueness, multiplicity, and other properties as positivity. Next, we will review and develop some numerical methods for solving the nonlinear Schrödinger equation, its time version, generalizations with rotational terms, and systems of NLSE (NLSS). We notice that the main problem to run numerical methods is the memory ...

Time series are useful for modeling systems behavior, for predicting some events (catastrophes, epidemics, weather, ...) or for classification purposes (pattern recognition, pattern analysis). Among the existing data analysis algorithms, ordinal pattern based algorithms have been shown effective when dealing with simulation data. However, when applied to quasi-periodically forced systems, they fail to detect SNA and tori as regular dynamics. In this work we address this concern by defining ordinal array (OA) based ...