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B. Craps, O. Evnin and J. Vanhoof, Renormalization, averaging, conservation laws and AdS (in)stability, JHEP 1501
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2015
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2015
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P. Gérard and S. Grellier, An explicit formula for the cubic Szegő equation, Trans. Amer. Math. Soc. 367
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P. Germain, Z. Hani and L. Thomann, On the continuous resonant equation for NLS: I. Deterministic analysis, J. Math. Pur. App. 105
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2016
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P. Germain and L. Thomann, On the high frequency limit of the LLL equation , Quart. Appl. Math. 74

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S. Kuksin and A. Maiocchi, The effective equation method
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2016
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P. Bizoń, B. Craps, O. Evnin, D. Hunik, V. Luyten and M. Maliborski, Conformal flow on S 3 S^{3} and weak field integrability in AdS 4 , Comm. Math. Phys. 353
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A. F. Biasi, J. Mas and A. Paredes, Delayed collapses of BECs in relation to AdS gravity, Phys. Rev. E 95
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2017
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A. Biasi, P. Bizoń, B. Craps and O. Evnin, Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates,
Original
2017
Later among the works it cites.
B. Craps, O. Evnin and V. Luyten, Maximally rotating waves in AdS and on spheres,

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2018

Solvable cubic resonant systems

Biasi, Anxo, Bizon, Piotr, Evnin, Oleg

Understand

Weakly nonlinear analysis of resonant PDEs in recent literature has generated a number of resonant systems for slow evolution of the normal mode amplitudes that possess remarkable properties.

Despite being infinite-dimensional Hamiltonian systems with cubic nonlinearities in the equations of motion, these resonant systems admit special analytic solutions, which furthermore display periodic perfect energy returns to the initial configurations.
Here, we construct a very large class of resonant systems that shares these properties that have so far been seen in specific examples emerging from a few standard equations of mathematical physics (the Gross-Pitaevskii equation, nonlinear wave equations in Anti-de Sitter spacetime).
Our analysis provides an additional conserved quantity for all of these systems, which has been previously known for the resonant system of the two-dimensional Gross-Pitaevskii equation, but not for any other cases.