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.
Author: T. B. Prayitno
Journal Code: jpfisikagg130019
