@article {26626,
	title = {Externally driven nonlinear Dirac equation revisited: Theory and simulations},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	volume = {52},
	year = {2019},
	pages = {155401},
	abstract = {The externally driven nonlinear Dirac (NLD) equation with\&nbsp;scalar-scalar\&nbsp; self-interaction studied in [J. Phys. A: Math. Theor. 49, 065402 (2016)] is revisited.\&nbsp;By using a variational method and an ansatz with five collective coordinates, the dynamics of the NLD solitons\&nbsp; is well described. It is shown that\&nbsp;this new ansatz possesses certain advantages, namely the canonical momentum agrees with the field momentum, the energy associated to the collective coordinate equations agrees with the energy of the NLD soliton, whereas the ansatz with either three or four collective coordinates does not.\&nbsp;Thus the study of the\&nbsp; whole phase space of the system is enhanced.\&nbsp;It is also shown that this approach is equivalent to the method of moments: the time variation of the charge,\&nbsp; the momentum, the energy, and the first moment\&nbsp; of the charge. The advantages of the new ansatz are illustrated by means of numerical simulations.\&nbsp;},
	url = {https://doi.org/10.1088/1751-8121/ab0dd9},
	author = {Niurka R. Quintero and Sihong Shao and Renato Alvarez-Nodarse and Franz G. Mertens}
}
