Spatiotemporal Binary Interaction and Designer quasi particle condensates

We introduce a new integrable model to investigate the dynamics of two component quasi particle condensates with spatio temporal interaction strengths. We derive the associated Lax-pair of the coupled GP equation and construct matter wave solitons. We show that the spatio temporal binary interaction strengths not only facilitate the stabilization of the condensates, but also enables one to fabricate condensates with desirable densities, geometries and properties leading to the so called "designer quasi particle condensates".