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The dark and bright solitons in different systems are already known inKlein-Gordon lattice. Instead of an external driving force, if the intrinsicfield is only considered, then the modal dynamics for small oscillations couldbe characterized by the bound state in a limited range of frequency, revealedvia associated Legendre polynomial. Bose Einstein condensation takes placearound bosonic particles having different wave functions within the boundstates in the temperature region T = 0 to Tc having implication for theeffective mass of the system. The pairing and interplay between the dark andbright solitons also occur with their effect on the condensation. Thiseffective mass is calculated via statistical mechanics route by two-partpartition function that also gives an indication for the transitiontemperature. The disappearance of the bound state after a critical frequency,or equivalently, after a critical temperature, gives rise to quasi-particles orphonons in the unbound states that propagate through the domains.

Effective Mass in Bose-Einstein Condensation in the Bound State and Phonon Propagation in the Unbound States