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  1. Normalized solutions for a fourth-order Schrödinger equation with a positive second-order dispersion coefficient

    In this paper, we study normalized solutions to a fourth-order Schrödinger equation with a positive second-order dispersion coefficient in the mass...

    **ao Luo, Tao Yang in Science China Mathematics
    Article 30 September 2022

  2. Ground state solution for a weighted fourth-order Schrödinger equation with exponential growth nonlinearity

    In this paper, we establish the existence of a ground state solution for a weighted fourth-order equation of Shrödinger type under boundary Dirichlet...

    Rima Chetouane, Brahim Dridi, Rached Jaidane in Lithuanian Mathematical Journal
    Article 01 October 2023

  6. Energy Scattering for Non-radial Inhomogeneous Fourth-Order Schrödinger Equations

    It is the goal of this manuscript to establish the scattering of global solutions to the following bi-harmonic Schrödinger equation, in the focusing...

    Tarek Saanouni, Binhua Feng in Mediterranean Journal of Mathematics
    Article 09 January 2024

  8. Global Well-posedness for the Fourth-order Defocusing Cubic Equation with Initial Data Lying in a Critical Sobolev Space

    This paper is devoted to study the Cauchy problem of the fourth-order defocusing, cubic equation iu t + Δ 2 u = − ∣ u ∣ 2 u in critical Sobolev space. We...

    Miao Chen, Hua Wang, **aohua Yao in Frontiers of Mathematics
    Article 30 June 2024

  9. Long-time behavior of solutions to a fourth-order nonlinear Schrödinger equation with critical nonlinearity

    We consider the long-time behavior of solutions to a fourth-order nonlinear Schrödinger (NLS) equation with a derivative nonlinearity. By using the...

    Mamoru Okamoto, Kota Uriya in Journal of Evolution Equations
    Article Open access 28 August 2021

  10. Exact Controllability of the Linear Biharmonic Schrödinger Equation with Space-Dependent Coefficients

    This paper deals with the exact boundary controllability of the linear fourth-order Schrödinger equation with space-dependent coefficients and...
    Kaïs Ammari, Hedi Bouzidi in Control and Inverse Problems
    Conference paper 2023

  11. Nodal Multi-peak Standing Waves of Fourth-Order Schrödinger Equations with Mixed Dispersion

    We consider the existence and concentration properties of standing waves for a fourth-order Schrödinger equation with mixed dispersion, which was...

    Yi He, **ao Luo, Vicenţiu D. Rădulescu in The Journal of Geometric Analysis
    Article Open access 10 December 2021

  12. Embedded Solitons of the Generalized Nonlinear Schrödinger Equation with High Dispersion

    The family of generalized Schrödinger equations is considered with the Kerr nonlinearity. The partial differential equations are not integrable by...

    Nikolay A. Kudryashov in Regular and Chaotic Dynamics
    Article 01 November 2022

  13. Riemann–Hilbert Problem Associated with the Fourth-Order Dispersive Nonlinear Schrödinger Equation in Optics and Magnetic Mechanics

    In this paper, by using Fokas method, we study the initial-boundary value problems (IBVPs) of the fourth-order dispersive nonlinear Schrödinger...

    Beibei Hu, Ling Zhang, ... Ning Zhang in Journal of Nonlinear Mathematical Physics
    Article Open access 17 August 2021

  14. Multi-Symplectic Simulation on Soliton-Collision for Nonlinear Perturbed Schrödinger Equation

    Seeking solitary wave solutions and revealing their interactional characteristics for nonlinear evolution equations help us lot to comprehend the...

    Peijun Zhang, Weipeng Hu, ... Zhijun Qiao in Journal of Nonlinear Mathematical Physics
    Article Open access 05 September 2023

  16. Tenth-Order Accurate Numerical Method for Solving the Time-Dependent Schrödinger Equation

    Abstract

    A tenth-order accurate method for the numerical solution of the time-dependent Schrödinger equation is presented. The method is based on the...

    M. A. Zakharov in Computational Mathematics and Mathematical Physics
    Article 01 February 2024

  17. The Frisch–Parisi Formalism for Fluctuations of the Schrödinger Equation

    We consider the solution of the Schrödinger equation u in \(\mathbb {R}\)...
    Sandeep Kumar, Felipe Ponce-Vanegas, ... Luis Vega in Mathematical Physics and Its Interactions
    Conference paper 2024

  19. Exact Boundary Controllability of the Linear Biharmonic Schrödinger Equation with Variable Coefficients

    In this paper, we study the exact boundary controllability of the linear fourth-order Schrödinger equation, with variable physical parameters and...

    Kaïs Ammari, Hedi Bouzidi in Journal of Dynamical and Control Systems
    Article 02 August 2022
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