# Chapter 12: On the energy cascade of acoustic wave turbulence: Beyond Kolmogorov-Zakharov solutions

In weak turbulence theory, the Kolmogorov-Zakharov spectra is a class of time-independent solutions to the kinetic wave equations. In this paper, we construct a new class of time-dependent solutions to those kinetic equations. These solutions exhibit the interesting property that the energy is cascaded from small wavenumbers to large wavenumbers. We can prove that starting … Continue reading Chapter 12: On the energy cascade of acoustic wave turbulence: Beyond Kolmogorov-Zakharov solutions

# Chapter 7: Coupling kinetic and Schrodinger equations – A simplified model by Soffer and Tran.

This post is based on my joint paper with Avy Soffer. When a bose gas is cooled below the Bose-Einstein critical temperature, the Bose-Einstein condensate is formed, consisting of a macroscopic number of particles, all in the ground state of the system. As we have already known from previous chapters (Chapters 1 &3), a finite … Continue reading Chapter 7: Coupling kinetic and Schrodinger equations – A simplified model by Soffer and Tran.