Abstract
Quantum mechanics equations for a system of the Bose particles are represented in the form of material field equations. A nonlinear equation for the macroscopic one-particle wave function is derived. Using the Krylov-Bogolyubov-Mitropol’skii method for equations in partial derivatives, nonlinear waves in the Bose-Einstein condensate are investigated. In the cubic approximation, dispersion relations for waves are derived and nonlinear frequency shift is calculated in the first- and third-order approximations for the interaction radius.
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