Geodesic
Construction of asymptotic solutions for weakly nonlinear Hamiltonian systems
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 14, Tome 140 (1984), pp. 36-40

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A change of variables is constructed for a class of weakly nonlinear Hamiltonian systems which makes it possible to reduce the order of the nonlinearity from $O(\varepsilon)$ to $O(\varepsilon^2)$ and to construct asymptotic solutions. The results can be applied to some nonlinear partial differential equations of interest in physics. 
@article{ZNSL_1984_140_a2,
     author = {S. A. Vakulenko},
     title = {Construction of asymptotic solutions for weakly nonlinear {Hamiltonian} systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {36--40},
     publisher = {mathdoc},
     volume = {140},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a2/}
}
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S. A. Vakulenko. Construction of asymptotic solutions for weakly nonlinear Hamiltonian systems. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 14, Tome 140 (1984), pp. 36-40. http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a2/