Exact Solutions for Solitary Waves in a Bose-Einstein Condensate under the Action of a Four-Color Optical Lattice

We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms the FOL which admits exact solitary-wave solutions. newly found class potentials includes more particular species, such as frustrated double-well superlattices, bichromatic three-color lattices, are subject to respective constraints. Our solutions provide options for controllable positioning density maxima localized patterns, Anderson-like localization in potential. A numerical is performed establish dynamical stability structural obtained solutions, makes them relevant experimental realization. offer applications design schemes quantum simulations processing information.