Solvable Cubic Resonant Systems View Full Text


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Article Info

DATE

2019-02-18

AUTHORS

Anxo Biasi, Piotr Bizoń, Oleg Evnin

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. More... »

PAGES

1-24

References to SciGraph publications

  • 2014-10. Renormalization group, secular term resummation and AdS (in)stability in JOURNAL OF HIGH ENERGY PHYSICS
  • 2015-01. Renormalization, averaging, conservation laws and AdS (in)stability in JOURNAL OF HIGH ENERGY PHYSICS
  • 2016. The Effective Equation Method in NEW APPROACHES TO NONLINEAR WAVES
  • 2017-08. Conformal Flow on S3 and Weak Field Integrability in AdS4 in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2019-02. On the Cubic Lowest Landau Level Equation in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2017-09. Maximally rotating waves in AdS and on spheres in JOURNAL OF HIGH ENERGY PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/s00220-019-03365-z

    DOI

    http://dx.doi.org/10.1007/s00220-019-03365-z

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112213786


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