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math.AP2023★ 3 cited
Exact Global Control of Small Divisors in Rational Normal Form
Jianjun Liu, Duihui Xiang
Rational normal form is a powerful tool to deal with Hamiltonian partial differential equations without external parameters. In this paper, we build rational normal form with exact…
math.AP2020
Birkhoff Normal Form for the Derivative Nonlinear Schrödinger Equation
Jianjun Liu
This paper is concerned with the derivative nonlinear Schrödinger equation with periodic boundary conditions. We obtain complete Birkhoff normal form of order six. As an applicatio…