Promoted analytical solutions of conformable Ginzburg-Landau applied in Bose-Einstein condensate with external potentials

This work concerns the construction of the approximate analytical solutions for the nonlinear complex conformable Ginzburg-Landau equations with external potential using the conformable residual series method. The governing model plays a pivotal role in modeling complex physical phenomena such as Bose-Einstein condensation and building approximate analytical solutions for this model, which is considered a distinctive addition given the scarcity of work presented in the literature in this context. The methodology lies in combines of generalized multivariable power series and residual error function. Convergence analysis is provided to illustrate the theoretical framework of our scheme in handling the projected nonlinear models. For a sake of practical computation, several naturalistic applications for Bose-Einstein condensates are examined involving zero trapping, periodic box, optical lattice, and harmonic potentials. In this orientation, numeric computations and graphical representations are provided to verify the correctness and accuracies of the tested applications. The dynamic behaviors of wave soliton solutions are captured at different parameters in addition to the comparison of acquired wave solutions with previous studies. The overall impact of this work lies in the ease with which the proposed approach can be applied to construct efficient and systematic approximate analytical solutions for complex nonlinear partial differential equations arising in quantum optics, quantum gases, quantum fluids, and other quantum mechanical phenomena.