Analytically and numerically, dispersive, weakly nonlinear wave packets are presented in a quasi-monochromatic medium

Abstract

This study applies computational and numerical techniques to develop some novel and accurate solutions for Gross–Pitaevskii (GP) equations. A quantum system of identical bosons is described using the Hartree–Fock approximation and pseudopotential interaction model by the Gross–Pitaevskii equation (GPE), named after Eugene P. Gross and Lev Petrovich Pitaevskii. Many solitary wave solutions are constructed in various forms based on the implementation of the Khater II method and the novel Kudryashov method. The gained solutions are numerically represented in various graph styles. The validity of the solutions is investigated by applying the septic-B-spline scheme based on calculating the requested conditions from the obtained computational solutions. To make our study more applicable, we study the stability of our solutions by focusing on the Hamiltonian system’s properties. Mathematica 13.1 checks all inputs and outcomes against the original model for further confidence.

Keywords

• Gross–Pitaevskii equation
• Ground state
• Quantum system
• Soliton
• Numerical solutions
• Stability