Article
Physics, Mathematical
Gino Biondini, Sitai Li, Dionyssios Mantzavinos
Summary: This study investigates the long-time behavior of solutions to the focusing nonlinear Schrodinger equation with symmetric, nonzero boundary conditions, exploring the nonlinear interactions between solitons and coherent oscillating structures. Combining inverse scattering transform and nonlinear steepest descent method, it reveals that the presence of a conjugate pair of discrete eigenvalues can lead to various outcomes such as soliton transmission, soliton trapping, or a mixed regime. The results are supported by accurate numerical simulations validating the soliton-induced position and phase shifts.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Astronomy & Astrophysics
Raquel Galazo-Garcia, Philippe Brax, Patrick Valageas
Summary: Fuzzy dark matter (FDM) models have self-similar solutions that differ greatly from the self-similar solutions of standard cold dark matter (CDM) models and do not converge to the latter in the semiclassical limit. These self-similar solutions in FDM models exhibit an inverse-hierarchy blowup, where larger masses become linear first, in contrast to the familiar CDM hierarchical collapse. This blowup process roughly follows the Hubble expansion and maintains a constant central density contrast over time, although the width of the self-similar profile shrinks in comoving coordinates.
Article
Multidisciplinary Sciences
Shariful Islam, Bishnupada Halder, Ahmed Refaie Ali
Summary: In this study, a unified method is used to find solutions for a nonlinear Schrödinger equation that describes the nonlinear spin dynamics of (2+1) dimensional Heisenberg ferromagnetic spin chains equation. The solutions are successfully constructed and the parametric requirements for the existence of a valid soliton are provided. 2D and 3D graphics are plotted to visualize some of the discovered solutions. The results of this investigation are potentially useful in understanding the physical significance of the model, especially in studying electrical solitons in nonlinear dispersive media.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics
Jonatan Lenells, Ronald Quirchmayr
Summary: The study focuses on the defocusing nonlinear Schrodinger equation in the quarter-plane, with decaying initial data and Dirichlet and Neumann boundary values approaching periodic single exponentials at large times. By utilizing Deift-Zhou steepest descent arguments, solutions are constructed and detailed formulas for their long-time asymptotics are obtained.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics
Zihua Guo, Chunyan Huang, Liang Song
Summary: In this note, we prove the pointwise decay in time of solutions to the 3D energy-critical nonlinear Schrodinger equations under the assumption of data in L1 and H3 norms. The key elements include the boundedness of the Schrodinger propagators in Hardy space established by Miyachi [9], and a fractional Leibniz rule in the Hardy space. We also extend the fractional chain rule to the Hardy space.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Physics, Multidisciplinary
Zhao Zhang, Biao Li, Abdul-Majid Wazwaz, Qi Guo
Summary: In this paper, a skillful partial limit approach is proposed to generate new solutions, called multiple-pole solutions, directly from the well-known N-soliton solution for the fifth-order modified Korteweg-de Vries equation. By applying the traditional limit method, the neglected dark double-pole solution is found. Additionally, a general method for constructing triple-pole solutions, multiple-pole solutions, and degeneration of breather solutions is creatively provided. Furthermore, the dynamic properties of these multiple-pole solutions are thoroughly discussed.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Applied
Bo Yang, Jianke Yang
Summary: We report new rogue wave patterns in the nonlinear Schrodinger equation that are formed by individual Peregrine waves. These patterns are described asymptotically by root structures of Adler-Moser polynomials and are much more diverse than previous rogue patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy. The analytical predictions of these patterns show good agreement with true solutions.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics
Oleg Avsyankin
Summary: This article discusses a second-order multidimensional integral equation with a homogeneous kernel of degree (-n). A special class of continuous functions with a given asymptotic behavior near zero is defined. It is proven that if the free term of the integral equation belongs to this class and the equation itself is solvable, then its solution also belongs to this class. To solve this problem, a special research technique is used, which is based on the decomposition of both the solution and the free term into spherical harmonics.
Article
Physics, Multidisciplinary
Bingwen Lin
Summary: The author examines the Darboux transformation and reduction conditions of three nonlocal NLS equations. The formulas for n-fold solutions are expressed in terms of determinants. Using these formulas, the author obtains explicit expressions for one- and twofold solutions of these nonlocal NLS equations, which exhibit singular and interesting structures. These types of solutions are novel for these nonlocal NLS equations.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Astronomy & Astrophysics
Tiago D. Ferreira, Joao Novo, Nuno A. Silva, A. Guerreiro, O. Bertolami
Summary: Nonminimally coupled curvature-matter gravity models offer an interesting alternative to address the dark energy and dark matter cosmological problems, with numerical tools using the imaginary-time propagation method showing the existence of static solutions even at low energy density regimes.
Article
Multidisciplinary Sciences
C. A. Onate, M. C. Onyeaju
Summary: The radial Schrodinger equation was solved using the supersymmetric approach and a combination of different potential models. Non-relativistic ro-vibrational energy spectra were obtained, along with an analysis of the variation of energy with parameters and thermal properties with temperature changes. The study showed that temperature has a positive effect on all thermal properties except the free energy.
Article
Mathematics
Christophe Charlier, Tom Claeys, Giulio Ruzza
Summary: This paper investigates the uniform asymptotics for deformed Airy kernel determinants, which have important mathematical and physical significance in finite temperature free fermion models and the narrow wedge solution of the Kardar-Parisi-Zhang equation.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
Luccas Campos
Summary: This study proves the scattering below the mass-energy threshold for a specific nonlinear Schrodinger equation, extending previous results and covering a broader range of parameter values and nonhomogeneous cases.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics
Luigi Appolloni, Simone Secchi
Summary: This study investigates the existence of solutions to the fractional nonlinear Schrodinger equation in the Sobolev space, proving the existence of a ground state solution and a multiplicity result in the radially symmetric case.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics
Jichao Wang, Ting Yu
Summary: In this paper, we study the singular perturbation problem for the Schrodinger-Poisson equation with critical growth. We establish the relationship between the number of solutions and the profiles of the coefficients when the perturbed coefficient is small. Additionally, we observe a different concentration phenomenon without any restriction on the perturbed coefficient and obtain an existence result.
