Some Comments of the Providing Masses of the Static Solitary Wave Solution of the One-Dimensional Gross-Pitaevskii Equation

Abstract: We have made some comments about the mass results of static solitary wave solutions of the one-dimensional Gross-Pitaevskii equation with time-dependent parabolic trap, time dependent scattering wave length of s-wave, and time-dependent external potential describing gain or loss term. Some written solutions of the equation were proposed by Atre et al. [Phys. Rev. E 73 (2006) 056611] which two of them based on the experimental results presented by Strecker et al. [Nature (London) 417 (2002) 150]. The solutions satisfy the condition of solitary wave solution since they are localized over all space. By this argument, the masses are obtained by integrating the Hamiltonian density over all space formulated in the Classical Field Theory. To calculate the masses, we construct the appropriate Lagrangian density representing the equation by initially writing the ansatz Lagrangian density and substituting  into Euler-Lagrange equation.  We find that two of them have the same masses and another should be  mathematically  have the pure imaginary function describing gain-loss term in order to keep mass to be real.

Keywords: Mass of solitary waves, Bose-Einstein Condensation, Gross-Pitaevskii

Author: T. B. Prayitno

Journal Code: jpfisikagg130019

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