Construction of quasi-periodic solutions for the quintic Schrödinger equation on the two-dimensional torus $\mathbb {T}^2$

DOI10.1090/TRAN/8329zbMath1478.37077OpenAlexW3164102792MaRDI QIDQ4992373

Min Zhang, Jian-guo Si

Publication date: 8 June 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/tran/8329

zbMATH Keywords

Birkhoff normal formquasi-periodic solutionsKAM theoryquintic Schrödinger equations

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items (5)

A KAM algorithm for two-dimensional nonlinear Schrödinger equations with spatial variable ⋮ Quasi-periodic solutions for quintic completely resonant derivative beam equations on T2 ⋮ Invariant tori for a two-dimensional completely resonant beam equation with a quintic nonlinear term ⋮ KAM tori for a two dimensional beam equation with a quintic nonlinear term and quasi-periodic forcing ⋮ KAM tori for the two-dimensional completely resonant Schrödinger equation with the general nonlinearity

Cites Work

• Energy supercritical nonlinear Schrödinger equations: quasiperiodic solutions
• Reducible quasi-periodic solutions for the non linear Schrödinger equation
• Resonant dynamics for the quintic nonlinear Schrödinger equation
• A KAM algorithm for the resonant non-linear Schrödinger equation
• An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation
• KAM for the nonlinear beam equation
• A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces
• Quasi-periodic solutions in a nonlinear Schrödinger equation
• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• KAM for the nonlinear Schrödinger equation
• Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
• Nearly integrable infinite-dimensional Hamiltonian systems
• Construction of periodic solutions of nonlinear wave equations in higher dimension
• A KAM theorem of degenerate infinite dimensional Hamiltonian systems. II
• Quasi-periodic solutions with Sobolev regularity of NLS on \(\mathbb T^d\) with a multiplicative potential
• KAM for beating solutions of the quintic NLS
• Growth of Sobolev norms for the quintic NLS on \(\mathbb T^2\)
• On invariant tori of full dimension for 1D periodic NLS
• Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential
• KAM tori for higher dimensional beam equations with constant potentials^*
• Newton's method and periodic solutions of nonlinear wave equations
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
• Quasi-Periodic Solutions for 1D Schrödinger Equations with Higher Order Nonlinearity
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