Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity
By Gerard Iooss, Pavel I. Plotnikov, J. Toland. 2005
169 citations recorded by the source corpus.
Subfields: Environmental Chemistry, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/516263c5105c65bac8db0e204a0991dfa883190d
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In Environmental Chemistry
In Statistical and Nonlinear Physics
- Massimiliano Berti
- Riccardo Montalto
- Pierre Baldi
- P. Bolle
- E. Haus
- Michela Procesi
- R. Feola
- Ivar Ekeland
Citations in the corpus
- Time quasi-periodic gravity water waves in finite depth (2017, background): “The existence of small amplitude time-periodic gravity standing wave solutions for bi-dimensional fluids has been first proved by Plotinkov and Toland [52] in finite depth and by Iooss, Plotnikov and Toland in [41] in infinite depth, see also [37], [38].”
- Cantor families of periodic solutions for completely resonant nonlinear wave equations (2004, background): “We also quote the recent papers [17]-[18] on the standing wave problem for a perfect fluid under gravity and with infinite depth which leads to a nonlinear and completely resonant second order equation.”
- Periodic solutions of fully nonlinear autonomous equations of Benjamin-Ono type (2012, methodology): “Following a suitable Nash-Moser scheme, we construct a sequence (un) ⊂ C ∞(T2) of ε-dependent trigonometric polynomials by setting u0 := v̄2 as defined in Section 5, h0 := 0, and un+1 := un + hn+1, hn+1 := −Πn+1Ψ̃nΦ̃n(Πn+1L̃4,nΠn+1) −1Πn+1Φ̃ −1 n M̃ −1 n Ψ̃ −1 n PεF (un), (9.5) provided that the inv”
- KAM for autonomous quasi-linear perturbations of mKdV (2014, result): “The name “descent method” has been used in Iooss–Plotnikov–Toland [16–18] to denote the iterative procedure of reduction of a linear differential (or pseudo-differential) operator with variable coefficients into one with constant coefficients, at any finite order of regularization, up to smoother re”
- A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations (2007, unknown): “This trick can sometimes simplify the computations (see for instance [8] and Remark 9 below).”