Construction of modulated amplitude waves via averaging in collisionally inhomogeneous Bose-Einstein condensates

Abstract

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 spatial and crossing zero. Infinitely many (positive measure set) modulated amplitude waves (periodic and quasi-periodic), which are instable, can be proved to exist by adjusting the intergration constant c on some open interval. Finally, some numerical simulations support our results.

arXiv comment13 pages, 2 figures

References in corpus (10)

• Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential
• Matter-wave solitons of collisionally inhomogeneous condensates
• Modulated Amplitude Waves and the Transition from Phase to Defect Chaos
• Stability criterion for bright solitary waves of the perturbed cubic-quintic Schroedinger equation
• Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates
• Solitary Waves Under the Competition of Linear and Nonlinear Periodic Potentials
• Resonant and Non-Resonant Modulated Amplitude Waves for Binary Bose-Einstein Condensates in Optical Lattices
• Modulated Amplitude Waves in Bose-Einstein Condensates
• Perturbation theory of dynamical systems
• Modulated amplitude waves with nonzero phases in Bose-Einstein condensates