Abstract

The research examines exact solutions which describe nonlinear differential equations that appear in quantum mechanics. The study centers on nonlinear Schrödinger equation (NLSE) and its multiple variants which include the Gross-Pitaevskii equation used for Bose-Einstein condensate simulations. We use classical methods which include the tanh-expansion technique and the Weierstrass elliptic function approach to produce explicit solutions. The methods enable us to manage the nonlinearity problems together with the dissipation elements which we encounter. We present soliton-like solutions for cubic NLSE which we analyze to determine their stability. The results extend previous works by incorporating dissipative effects which provide new understanding of quantum systems that exhibit interactions. The analysis holds importance for quantum optics research and condensed matter physics applications.