Soliton dynamics with time-dependent neural quantum states

Abstract

A variational approach based on Neural Quantum States is used to simulate the real-time dynamics of bright and dark solitons in the one-dimensional Gross–Pitaevskii equation. In this framework, the condensate wavefunction is represented by a complex-valued neural network, whose parameters are evolved according to the Time-Dependent Variational Principle. This method provides a flexible neural network representation of the wavefunction and it is validated against analytical benchmarks to assess its accuracy and stability. The developed tool captures the main dynamics of several scenarios, including stationary soliton preparation, single soliton propagation, and two soliton interaction and collision processes. These examples serve as proof of principle to explore the capacity of Neural Quantum States to represent time-dependent nonlinear wavefunctions, highlighting their potential as a flexible variational framework for nonlinear quantum dynamics