Results 61 to 70 of about 2,498 (146)

Scattering and Blow‐Up Dichotomy of the Energy‐Critical Nonlinear Schrödinger Equation With the Inverse‐Square Potential

Mathematical Methods in the Applied Sciences, Volume 48, Issue 8, Page 9225-9240, 30 May 2025.
ABSTRACT In this paper, we consider the energy critical nonlinear Schrödinger equation with a repulsive inverse square potential. In particular, we deal with radial initial data, whose energy is equal to the energy of static solution to the corresponding nonlinear Schrödinger equation without a potential.
Masaru Hamano, Masahiro Ikeda
wiley   +1 more source

Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics

Journal of Advanced Research, 2019
In nonlinear optics, the soliton transmission in different forms can be described with the use of nonlinear Schrödinger (NLS) equations. Here, the soliton transmission is investigated by solving the NLS equation with the reciprocal of the group velocity ...
Weitian Yu, Qin Zhou, Mohammad Mirzazadeh, Wenjun Liu, Anjan Biswas   +4 more
doaj   +1 more source

The conservative Camassa–Holm flow with step‐like irregular initial data

Proceedings of the London Mathematical Society, Volume 130, Issue 5, May 2025.
Abstract We extend the inverse spectral transform for the conservative Camassa–Holm flow on the line to a class of initial data that requires strong decay at one endpoint but only mild boundedness‐type conditions at the other endpoint. The latter condition appears to be close to optimal in a certain sense for the well‐posedness of the conservative ...
Jonathan Eckhardt, Aleksey Kostenko
wiley   +1 more source

On Blow-Up and Explicit Soliton Solutions for Coupled Variable Coefficient Nonlinear Schrödinger Equations

Mathematics
This work is concerned with the study of explicit solutions for a generalized coupled nonlinear Schrödinger equations (NLS) system with variable coefficients.
José M. Escorcia, Erwin Suazo
doaj   +1 more source

Deformation conjecture: deforming lower dimensional integrable systems to higher dimensional ones by using conservation laws

Journal of High Energy Physics, 2023
Utilizing some conservation laws of (1+1)-dimensional integrable local evolution systems, it is conjectured that higher dimensional integrable equations may be regularly constructed by a deformation algorithm.
S. Y. Lou, Xia-zhi Hao, Man Jia
doaj   +1 more source

On the wave turbulence theory of 2D gravity waves, I: Deterministic energy estimates

Communications on Pure and Applied Mathematics, Volume 78, Issue 2, Page 211-322, February 2025.
Abstract Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV‐type equations. However, our situation
Yu Deng, Alexandru D. Ionescu, Fabio Pusateri   +2 more
wiley   +1 more source

Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials

Results in Physics, 2019
We consider coupled nonlinear Schrodinger equation (CNLSE) of the Gross-Pitaevskii-type, with linear mixing and nonlinear cross-phase modulation. Motivated by the study of matter waves in Bose-Einstein condensates and multicomponent (vectorial) nonlinear
Hamdy I. Abdel-Gawad, A. Biswas, A.S. Alshomrani, M. Belic   +3 more
doaj   +1 more source

Bifurcation, Chaotic, Sensitivity Analysis, and Optical Soliton Profiles for the Spin Hirota–Maxwell–Bloch Equation in an Erbium‐Doped Fiber

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
In this work, the reduced spin Hirota–Maxwell–Bloch (rsHMB) equation is examined analytically. This model is useful for characterizing the propagation of femtosecond pulses in an erbium‐doped fiber. The optical soliton solutions of the introduced rsHMB problem are constructed using the Jacobi elliptic function (JEF) expansion technique.
Asma Taskeen, Muhammad Ozair Ahmed, Muhammad Zafarullah Baber, Baboucarr Ceesay, Nauman Ahmed, Zine El Abiddine Fellah   +5 more
wiley   +1 more source

Algebraic Lower Bounds on the Spatial Analyticity Radius for Higher Order Nonlinear Schrödinger Equations

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
We investigate the initial value problem associated to the higher order nonlinear Schrödinger equation i∂tu+−1j+1∂x2ju=u2ju x,t≠0∈ℝ,ux,0=u0x, where j ≥ 2 is any integer, u is a complex valued function, and the initial data u0 is real analytic on ℝ and has a uniform radius of spatial analyticity σ0 in the space variable.
Tegegne Getachew, Birilew Belayneh, Betre Shiferaw, Huaiqin Wu   +3 more
wiley   +1 more source

Efficient numerical approximations for a nonconservative nonlinear Schrödinger equation appearing in wind‐forced ocean waves

Studies in Applied Mathematics, Volume 153, Issue 4, November 2024.
Abstract We consider a nonconservative nonlinear Schrödinger equation (NCNLS) with time‐dependent coefficients, inspired by a water waves problem. This problem does not have mass or energy conservation, but instead mass and energy change in time under explicit balance laws.
Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza   +2 more
wiley   +1 more source