Theoretical Investigation Of Solitons In Bose-einstein Condensates. Analytical And Numerical Solution To The Gross-Pitaevskii Equation (a Nonlinear Partial Differential Equation)

      Аннотация: The presence of solitons in bose-einstein condensates can be studied using nonlinear partial differential equation called the gross-pitaevskii equation. An analytical technique using darboux transformation with the lax technique is attempted. The best possible numerical technique among the split-step fourier method, crank nicolson finite difference method and the split-step crank nicolson method was analysed based on the merits and demerits of each method. Finally after both an analytical and numerical analysis of the gross-pitaevskii equation, the ideal conditions for the formation of various types of solitons were identified.

Ключевые слова: Bose-Einstein condensates, solitons, NON LINEAR PARTIAL DIFFERENTIAL EQUATIONS, DARBOUX TRANSFORMATION