REVIEW 3 cited by
Solvable cubic resonant systems
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Solvable cubic resonant systems
read the original abstract
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.
Forward citations
Cited by 3 Pith papers
-
Random matrix theory of integrability-to-chaos transition
Level-spacing distributions in the quantum integrability-to-chaos transition are controlled by the unordered sample of off-diagonal matrix elements of the perturbation in the integrable eigenbasis, yielding a predicti...
-
A superintegrable quantum field theory
The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.
-
Quantum estimates for classical polynomial optimization
A quantum-variational matrix method is proposed for bounding homogeneous polynomials, with converging numerical tensor-eigenvalue estimates and a new conjectured inequality for Biasi's resonant Hamiltonians.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.