First and second order approximations for a nonlinear wave equation

N.N. Bogolyubov, Yu. A. Mitropol’skii Asymptotic Methods in the Theory of Nonlinear Oscillations,

1958

Earlier work this paper cites.

P. Lax, Integral of nonlinear equations of evolution and solitary waves,

1968

Earlier work this paper cites.

L.-Y. Chen, N. Goldenfeld, Y. Oono, Renormalization group theory for global asymptotic analysis,

1994

Earlier work this paper cites.

L.-Y. Chen, N. Goldenfeld, Y. Oono, Renormalization group and singular perturbations: multiple scales, boundary layers, and reductive perturbation theory,

1996

Earlier work this paper cites.

I. Moise, R. Temam, Renormalization group method. Applications to Navier– Stokes equation,

2000

Earlier work this paper cites.

M. Ziane, On a certain renormalization group method,

2000

Earlier work this paper cites.

I. Moise, M. Ziane, Renormalization Group Method. Applications to Partial Differential Equations,

2001

Earlier work this paper cites.

R. Temam, D. Wirosoetisno, Averaging of differential equations generating oscillations and an application to control,

2002

Cited alongside, same era.

N. Burq, P. Gérard, N. Tzvetkov, Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces,

2005

Cited alongside, same era.

M. Petcu, R. Temam, D. Wirosoetisno, Renormalization group method applied to the primitive equations,

2005

Cited alongside, same era.

R. De Ville, A. Harkin, M. Holzer, K. Josic, T. Kaper, Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations,

2008

Cited alongside, same era.

P. Germain, N. Masmoudi, J. Shatah, Global solutions for the gravity water waves equation in dimension 3,

2009

Cited alongside, same era.

S. Gustafson, K. Nakanishi, T.-P. Tsai, Scattering theory for the Gross-Pitaevskii equation in three dimensions,

2009

Later among the works it cites.

W.K. Abou Salem, On the renormalization group approach to perturbation theory for PDEs,

2010

Later among the works it cites.

J. Colliander, M.Keel, G. Staffilani, H. Takaoka, T. Tao, Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation,

2010

Later among the works it cites.

P. Gérard, S. Grellier, The cubic Szegö equation,

2010

Later among the works it cites.

J. Shatah, Space-time resonances,

2010

Later among the works it cites.

O. Pocovnicu, Explicit formula for the solution of the Szegö equation on the real line and applications,

2011