By Dmitry E. Pelinovsky

This e-book presents a entire therapy of the Gross–Pitaevskii equation with a periodic strength; particularly, the localized modes supported via the periodic strength. It takes the mean-field version of the Bose–Einstein condensation because the start line of research and addresses the lifestyles and balance of localized modes. The mean-field version is simplified additional to the coupled nonlinear Schrödinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schrödinger equations. one of many vital positive factors of such platforms is the lifestyles of band gaps within the wave transmission spectra, which aid desk bound localized modes referred to as the distance solitons. those localized modes recognize a stability among periodicity, dispersion and nonlinearity of the actual approach. Written for researchers in utilized arithmetic, this e-book as a rule makes a speciality of the mathematical homes of the Gross–Pitaevskii equation. It additionally serves as a reference for theoretical physicists drawn to localization in periodic potentials.

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