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We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…

Quantum Physics · Physics 2009-11-10 A. D. Alhaidari

We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schr\"odinger equations with super-quadratic confinement in two and three spatial dimensions. These solutions are given by time-dependent rotations of…

Analysis of PDEs · Mathematics 2024-11-28 Irina Nenciu , Xiaoan Shen , Christof Sparber

We consider travelling periodical and quasiperiodical waves in single mode fibres, with weak birefringence and under the action of cross-phase modulation. The problem is reduced to the ``1:2:1" integrable case of the two-particle quartic…

High Energy Physics - Theory · Physics 2019-08-15 P L Christiansen , J C Eilbeck , V Z Enolskii , N A Kostov

In this paper, we study normalized solutions to the Chern-Simons-Schr\"odinger system, which is a gauge-covariant nonlinear Sch\"oridnger system with a long-range electromagnetic field, arising in nonrelativistic quantum mechanics theory.…

Analysis of PDEs · Mathematics 2020-12-21 Tianxiang Gou , Zhitao Zhang

The semi-classical regime of standing wave solutions of a Schr\"odinger equation in presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is show that there exists a…

Analysis of PDEs · Mathematics 2009-11-13 Silvia Cingolani , Simone Secchi , Marco Squassina

In this paper, by adapting the perturbation method, we study normalized standing wave solutions for the following nonlinear Schr\"odinger-Bopp-Podolsky system: - Delta u + q(x) phi u = omega u + f(u) in Omega, - Delta phi + a^2 Delta^2 phi…

Analysis of PDEs · Mathematics 2026-02-23 Kai Sheng

The time-global existence of solutions to a system of stochastic Schr\"odinger equations with multiplicative noise and the quadratic nonlinear terms are discussed in this paper. The same system in the deterministic treatment was studied in…

Analysis of PDEs · Mathematics 2023-05-30 Masaru Hamano , Shunya Hashimoto , Shuji Machihara

We present the bound state solutions of the Schr\"odinger equation with generalized inverted hyperbolic potential using the Nikiforov-Uvarov method. We obtain the energy spectrum and the wave function with this potential for arbitrary -…

Mathematical Physics · Physics 2015-05-30 Akpan N. Ikot , Oladunjoye A. Awoga , Louis E. Akpabio , Benedict I. Ita

We consider parabolic Schr\"odinger type equations associated to fractional powers of uniformly elliptic 2m-order operators with constant coefficients. Potentials and initial data are considered in suitable Morrey spaces. By means of…

Analysis of PDEs · Mathematics 2024-07-24 Jan W. Cholewa , Anibal Rodriguez-Bernal

We prove the existence of a $L^2$-normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the…

Analysis of PDEs · Mathematics 2020-10-28 Margherita Nolasco

The paper addresses an open problem raised in [Bartsch, Molle, Rizzi, Verzini: Normalized solutions of mass supercritical Schr\"odinger equations with potential, Comm. Part. Diff. Equ. 46 (2021), 1729-1756] on the existence of normalized…

Analysis of PDEs · Mathematics 2023-06-14 Thomas Bartsch , Shijie Qi , Wenming Zou

We present analytically the exact energy bound-states solutions of the Schrodinger equation in D-dimensions for a recently proposed modified Kratzer potential plus ring-shaped potential by means of the conventional Nikiforov-Uvarov method.…

Quantum Physics · Physics 2009-11-13 Sameer M. Ikhdair , Ramazan Sever

We study propagation of stationary waves in disordered non-linear media described by the non-linear Schroedinger equation and show that for given boundary conditions and a given coherent wave incident on a sample the number of solutions of…

Disordered Systems and Neural Networks · Physics 2009-11-10 B. Spivak , A. Zyuzin

This paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of…

Dynamical Systems · Mathematics 2024-06-19 Hui Wei , Shuguan Ji

We investigate rogue-wave solutions in a three-component coupled nonlinear Schrodinger equation. With certain requirements on the backgrounds of components, we construct a multi-rogue-wave solution that exhibits a structure like a…

Pattern Formation and Solitons · Physics 2015-01-26 Li-Chen Zhao , Jie Liu

This paper investigates the existence of normalized solutions for the following Chern-Simons-Schr\"odinger equation: \begin{equation*} \left\{ \begin{array}{ll} -\Delta u+\lambda u+\left(\frac{h^{2}(\vert x\vert)}{\vert…

Analysis of PDEs · Mathematics 2025-05-01 Chenlu Wei , Sitong Chen , Xinao Zhou

We consider the Schrodinger equation with a logarithmic nonlinearity and a repulsive harmonic potential. Depending on the parameters of the equation, the solution may or may not be dispersive. When dispersion occurs, it does with an…

Numerical Analysis · Mathematics 2023-12-04 Remi Carles , Chunmei Su

From the algebraic treatment of the quasi-solvable systems, and a q-deformation of the associated $su(2)$ algebra, we obtain exact solutions for the q-deformed Schrodinger equation with a 3-dimensional q-deformed harmonic oscillator…

High Energy Physics - Theory · Physics 2007-05-23 Abilio De Freitas , Sebastian Salamo

In recent times it has been paid attention to the fact that (linear) wave equations admit of "soliton-like" solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized…

Quantum Physics · Physics 2012-05-18 Michel Zamboni-Rached , Erasmo Recami

An efficient method is proposed for numerical solutions of nonlinear Schr\"{o}dinger equations in an unbounded domain. Through approximating the kinetic energy term by a one-way equation and uniting it with the potential energy equation,…

Numerical Analysis · Mathematics 2009-11-13 Jiwei Zhang , Zhenli Xu , Xiaonan Wu