In this paper, we propose three new types of the integrable nonlocal combined nonlinear Schrödinger–Gerdjikov–Ivanov (NLS-GI) models. Focusing NLS equation: Long-time dynamics of step-like initial data. We show that there are three regions in the half-plane −∞ < x < ∞, t > 0. We consider the Cauchy problem for the defocusing nonlinear Schrödinger (NLS) equation for finite density type initial data. when is victoria day in 2025 Many organizations are leveraging data analytics to make informed business decisions, leading to. In a recent paper, we presented the long-time asymptotics of the solution of this problem along the rays , where is a constant. We consider the modified Korteweg–de Vries equation on the line. Results for Quasi-Periodic Data on R u 0(x) = acos(x) + bcos(p 2x) Tadahiro Oh: Local existence proved for quasi-periodic data and global existence for a class of limit periodic data. Feb 10, 2021 · Long-Time Asymptotics for the Integrable Nonlocal Focusing Nonlinear Schrödinger Equation for a Family of Step-Like Initial Data. uche ojeh net worth On one hand, as for Euclidean case, we discuss problems including the Critical norm conjecture for high dimensional inter-critical NLS and the Dynamics of We consider the focusing nonlinear Schrödinger equation on the quarter plane. In today’s fast-paced business environment, effective communication and visual representation of organizational structures are vital. We produce a family of matrix Riemann–Hilbert (RH) problems parametrized by a given scalar function r(k). In this article, we study long time dynamics for defocusing cubic nonlinear Schrödinger equations (NLS) on three dimensional product space. 2) with A1 = A2, φ1,φ2 ∈ R, and B1 = B2 = 0 was presented in [4], and was further developed in [5,6]. los angeles time now am or pm in california In this paper, we propose three new types of the integrable nonlocal combined nonlinear Schrödinger–Gerdjikov–Ivanov (NLS-GI) models. ….

Our main … Expand Focusing NLS equation: long-time dynamics of step-like initial data AB De Monvel, VP Kotlyarov, D Shepelsky International Mathematics Research Notices 2011 (7), 1613-1653 , 2011 For step like initial data we show that the solution decomposes for long times in three main regions: - a region where solitons and breathers travel with positive velocities on a constant background c_+; - an expanding oscillatory region that can contain generically breathers; - a region of breathers travelling with negative velocities on the. Feb 1, 2024 · Particularly, since the RH problem is equivalent to Gel’fand–Levitan–Marchenko (GLM) theory, we can obtain the soliton solution of nonlocal DNLS equation (1. 1007/s00220-021-03946-x Corpus ID: 213178109; The Focusing NLS Equation with Step-Like Oscillating Background: Scenarios of Long-Time Asymptotics @article{Monvel2020TheFN, title={The Focusing NLS Equation with Step-Like Oscillating Background: Scenarios of Long-Time Asymptotics}, author={A D. In today’s digital age, data plays a crucial role in decision-making and business strategies. aryna sabalenka boyfriend age The pure soliton solutions of the NK-NLS equation with nonzero boundary conditions are obtained in [23]. The multi-soliton solutions can be given via the Hirota bilinear method. In this paper we study long time dynamics (i, scattering and blow-up) of solutions for the focusing NLS with a repulsive inverse-power po-tential and with initial data lying exactly at the mass-energy threshold, namely, when EV (u0)M(u0) = E0(Q)M(Q). Long-time behavior of the solution to the mKdV equation in the case cl > cr = 0 and t → ∞ was studied recently in Kotlyarov and Minakov (2010 J Phys. comal isd school calendar 2024 2025 Online news platforms have emerged as a popular alternative to traditional media out. 2) for q(x,0) can be transformed into the step-like initial data for ρ(x,0) and v(x. Of particular interest to us is the work [33], where Jenkins derived detailed formulas for the long-time asymptotics for the defocusing NLS equation with step-like initial data of the. Jenkins , Fromm, Lenells, and Quirchmayr further investigated the long-time asymptotics of the solutions of the NLS equation for different step-like initial data. In this paper, we study large-time asymptotics for the complex modified Korteveg–de Vries equation with step-like initial data. We produce a family of matrix Riemann–Hilbert (RH) problems parametrized by a given scalar function r(k). columbus crew club america draw Long-Time Asymptotics for the Integrable Nonlocal Focusing Nonlinear Schrödinger Equation for a Family of Step-Like Initial Data. ….

For the initial data in the Schwarz space S (R) and using the IST method, Zakharov and Manakov obtained the long-time asymptotics of the NLS equation [23] q (x, t) = t − 1 / 2 h (x / t) e i x 2 4 t ± 2 i | h (x / t) | 2 log ⁡ t + O (t − 3 / 2. The paper aims at studying the long-time asymptotics of the solution to this problem. The results … We undertake a comprehensive study for the fractional nonlinear Schrodinger equation \begin{document}$ i\partial_t u - (-\Delta)^s u = \mu_1 |u|^{\alpha_1} u + \mu_2. what time is us vs serbia 2) with the initial value condition satis ed (1 Oct 22, 2017 · We study the initial value problem for the integrable nonlocal nonlinear Schrodinger (NNLS) equation iqt(x,t)+qxx(x,t)+2σq2(x,t) q¯ (−x,t)=0 with decaying (as x → ±∞) boundary conditions. Thus, the expression of the long-time asymptotic solution of the RH problem is solved accurately. Jun 1, 2020 · In a recent paper, we presented scenarios of long-time asymptotics for a solution of the focusing nonlinear Schrödinger equation whose initial data approach two different plane waves. what is the molar mass of copper