2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57793First we show through a simulation that a massive Schwinger model used to formulate solutions to charge density wave transport is in itself insufficient for transport of solitons (anti solitons) through a pinning gap model of charge density wave transport. We show that a model Hamiltonian with Peierls condensation energy used to couple adjacent chains (or transverse wave vectors ) permits formation of solitons (anti solitons) which could be used to transport charge density waves through a potential barrier . We argue that there are analogies between this construction and the false vacuum hypothesis used for showing a necessary and sufficient condition for formation of charge density wave soliton - anti soliton pairs in wave functionals presented in a prior publication via use of the Bogomil'nyi inequality39 pages, 8 figures : IJMPB - Accepted ArticleMathematical Physics65Z05 ; 81S99text