Vladimir Zakharov was Regent’s Professor Emeritus at University of Arizona, Tucson, USA. He published nine books and around 400 articles in peer reviewed journals, see math.arizona.edu/~zakharov/Victor Lvov is consultant at the Weizmann Institute of Science. He published three books and above 270 articles in peer reviewed journals, see weizmann.ac.il/chembiophys/lvov/ and in wikipedia.org/wiki/Victor_L%27vovGregory Falkovich is a professor at the Weizmann Institute of Science, he published three books and around 200 articles in peer reviewed journals, weizmann.ac.il/complex/falkovich/

• O. Introduction.- 1. Equations of Motion and the Hamiltonian Formalism.- 2. Statistical Description of Weak Wave Turbulence.- 3. Stationary Spectra of Weak Wave Thrbulence.- 4. The Stability Problem and Kolmogorov Spectra.- 5. Physical Applications .- 6. Conclusion.- A. Appendix.- A.1 Variational Derivatives.- A.2 Canonicity Conditions of Transformations.- A.3 Elimination of Nonresonant Terms from the Interaction Hamiltonian .- A.4 Feynman rules and derivation of the renormalized kinetic equations.- A.5 Liouville approach and derivation of the Master Equation.

Vladimir Zakharov was Regent’s Professor Emeritus at University of Arizona, Tucson, USA. He published nine books and around 400 articles in peer reviewed journals, see math.arizona.edu/~zakharov/Victor Lvov is consultant at the Weizmann Institute of Science. He published three books and above 270 articles in peer reviewed journals, see weizmann.ac.il/chembiophys/lvov/ and in wikipedia.org/wiki/Victor_L%27vovGregory Falkovich is a professor at the Weizmann Institute of Science, he published three books and around 200 articles in peer reviewed journals, weizmann.ac.il/complex/falkovich/

• O. Introduction.- 1. Equations of Motion and the Hamiltonian Formalism.- 2. Statistical Description of Weak Wave Turbulence.- 3. Stationary Spectra of Weak Wave Thrbulence.- 4. The Stability Problem and Kolmogorov Spectra.- 5. Physical Applications .- 6. Conclusion.- A. Appendix.- A.1 Variational Derivatives.- A.2 Canonicity Conditions of Transformations.- A.3 Elimination of Nonresonant Terms from the Interaction Hamiltonian .- A.4 Feynman rules and derivation of the renormalized kinetic equations.- A.5 Liouville approach and derivation of the Master Equation.

Vladimir Zakharov was Regent’s Professor Emeritus at University of Arizona, Tucson, USA. He published nine books and around 400 articles in peer reviewed journals, see math.arizona.edu/~zakharov/Victor Lvov is consultant at the Weizmann Institute of Science. He published three books and above 270 articles in peer reviewed journals, see weizmann.ac.il/chembiophys/lvov/ and in wikipedia.org/wiki/Victor_L%27vovGregory Falkovich is a professor at the Weizmann Institute of Science, he published three books and around 200 articles in peer reviewed journals, weizmann.ac.il/complex/falkovich/

• O. Introduction.- 1. Equations of Motion and the Hamiltonian Formalism.- 2. Statistical Description of Weak Wave Turbulence.- 3. Stationary Spectra of Weak Wave Thrbulence.- 4. The Stability Problem and Kolmogorov Spectra.- 5. Physical Applications .- 6. Conclusion.- A. Appendix.- A.1 Variational Derivatives.- A.2 Canonicity Conditions of Transformations.- A.3 Elimination of Nonresonant Terms from the Interaction Hamiltonian .- A.4 Feynman rules and derivation of the renormalized kinetic equations.- A.5 Liouville approach and derivation of the Master Equation.