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  1. No Access

    Article

    Whiskered Tori for Forced Beam Equations with Multi-dimensional Liouvillean Frequency

    In this paper we develop a Kolmogorov–Arnold–Moser (KAM) theory close to two fixed points for quasi-periodically forced nonlinear beam equation $$\begin{aligned} \begin{aligned} y_{tt}+my+y_{xxxx}=y^{3}+ \varepsi...

    Hongyu Cheng, Wen Si, Jianguo Si in Journal of Dynamics and Differential Equations (2020)

  2. No Access

    Article

    Periodic and Quasi-Periodic Solutions for Reversible Unbounded Perturbations of Linear Schrödinger Equations

    In this paper, we consider a new class of derivative nonlinear Schrödinger equations with reversible nonlinearities of the form $$\begin{aligned} \mathrm {i}u_t+u_{xx}+|u_x|^{4}u=0,\quad (t, x)\in {\mathbb {R}}\t...

    Zhaowei Lou, Jianguo Si in Journal of Dynamics and Differential Equations (2020)

  3. No Access

    Article

    Quasi-Periodic Solutions for the Reversible Derivative Nonlinear Schrödinger Equations with Periodic Boundary Conditions

    In this paper, we prove the existence of small amplitude, smooth time quasi-periodic solutions for a class of reversible derivative nonlinear Schrödinger equations with periodic boundary conditions. The proof ...

    Zhaowei Lou, Jianguo Si in Journal of Dynamics and Differential Equations (2017)

  4. Article

    Open Access

    An anisotropic quasilinear problem with perturbations

    This work focuses on proving the existence and uniqueness of strong solutions of perturbed anisotropic total variation flow with the Neumann boundary condition when the initial data is an

    Jie Rui, Jianguo Si in Boundary Value Problems (2013)

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