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We apply the averaging method to analyze spatio-temportal structures in nonlinear Schrödinger equations and thereby study the dynamics of quasi-one-dimensional collisionally inhomogeneous Bose–Einstein condensates with the scattering length varying periodically in space and crossing zero. Infinitely many modulated amplitude waves with nontrivial phases are shown.

Construction of Modulated Amplitude Waves via Averaging in Collisionally Inhomogeneous Bose–Einstein Condensates