Schrodingers_Equation

Schrodingers' Equation

Intro

The one-dimensional nonlinear Schrodinger equation is a classical field equation that is used to study quantum mechanical systems, including nonlinear wave propagation in optical fibers and/or waveguides, Bose-Einstein condensates, and plasma waves. The nonlinear 1-D Schrodinger equation is:

$$i\frac{\partial h}{\partial t} + 0.5\frac{\partial^2 h}{\partial x^2} + |h|^2h = 0$$

Data Prepration

In this case a periodic boundary condition was used

$$\begin{aligned} h(0, x) &= 2sech(x)\\\ h(t, -5) &= h(t, 5)\\\ h_x(t, -5) &= h_x(t, 5) \end{aligned}$$

Parameter Study

This case was solved using L-BFGS optimization method.

Convergence animation	LBFGS, 6.9k, Loss 1.47e-5

Acknowledgement

1. plotting functions were taken from PINN