Damped schrodinger equation
WebAdvances in Differential Equations. We consider the Cauchy problem for the $L^{2}$-critical damped nonlinear Schrödinger equation. WebJan 31, 2024 · We consider the Cauchy problem for linearly damped nonlinear Schrödinger equations. i ∂ t u + Δ u + i a u = ± u α u, ( t, x) ∈ [ 0, ∞) × R N, where a > 0 and α > 0. We prove the global existence and scattering for a sufficiently large damping parameter in the energy-critical case. We also prove the existence of finite time blow ...
Damped schrodinger equation
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WebOct 31, 2024 · [1] B. Alouini, Finite dimensional global attractor for a damped fractional anisotropic Schrödinger type equation with harmonic potential, Commun.Pure Appl. Anal., 19 (2024), 4545-4573. doi: 10.3934/cpaa.2024206. [2] W. Bao and Q. Du, Computing the ground state solution of Bose–Einstein condensates by a normalized gradient flow, SIAM … WebJan 1, 2004 · In [25], the global existence and blowup of solutions for damped nonlinear Schrödinger equation is analytically investigated, and [1] introduces an extension of the time-splitting sine-spectral...
WebOct 17, 2024 · Abstract: We prove spatiotemporal algebraically decaying estimates for the density of the solutions of the linearly damped nonlinear Schrödinger equation with … WebJul 31, 2024 · As an aside, I am worried about your equation. If I prepare a damped harmonic oscillator in the state $( 0> + N> )/ \sqrt{2}$ where N is some colossal number of photons, then I expect to find that I very rapidly evolve into a statistically mixed state, $\rho(t) \sim ( 0><0 + N>
WebAbstract This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrödinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant. WebLogarithmic decay for damped hypoelliptic wave and Schrödinger equations Camille Laurent∗and Matthieu Léautaud† June 11, 2024 Abstract We consider damped wave (resp. Schrödinger and plate) equations driven by a hypoelliptic “sum of squares” operator L on a compact manifold and a damping function b(x). We assume the Chow-
WebJan 17, 2024 · In this paper, we consider the well-posedness of the weakly damped stochastic nonlinear Schrödinger(NLS) equation driven by multiplicative noise. First, we show the global existence of the unique solution for the damped stochastic NLS equation in critical case. Meanwhile, the exponential integrability of the solution is proved, which …
WebMay 22, 2008 · The following coupled damped Klein-Gordon-Schrödinger equations are considered i\psi_ {t} +\triangle\psi + i\alpha \psi ^ {2}\psi = \phi\psi\,\, {\rm in}\,\,\Omega \times (0,\infty), (\alpha > 0) \phi_ {tt} - \triangle\phi + a (x)\phi_ {t} = \psi ^ {2} {\mathcal {X}}_ {\omega}\, {\rm in}\,\Omega \times (0,\infty), flu injection cpt codeWebJun 9, 2015 · We investigate the initial value problem for a semi-linear fractional damped Schrödinger equation. Global existence and scattering are proved depending on the … flu injection melbourneWebMar 1, 2024 · odinger equation (NLS) has been applied widely to simulate the evolution of wa ve packets in nonlinear and dispersive media. It can describe man y … green faculty pte ltdWebApr 1, 2024 · The damped nonlinear Schrödinger (DNLS) equation is (1) i ψ t + Δ ψ + β ψ 2 ψ + i γ ψ = 0, where ψ ( x, t) is a complex function with x = ( x 1, …, x d) ⊤ ∈ R d and t … green faded backgroundWebMar 24, 2024 · The Schrödinger equation describes the motion of particles in nonrelativistic quantum mechanics, and was first written down by Erwin Schrödinger. The time … flu injection formWebJun 9, 2015 · We investigate the initial value problem for a semi-linear fractional damped Schrödinger equation. Global existence and scattering are proved depending on the size of the damping coefficient. Acknowledgments T. Saanouni is grateful to the Laboratory of PDE and Applications at the Faculty of Sciences of Tunis. REFERENCES 1. flu injections toowoombaWebAug 28, 2024 · In a recent manuscript [ 6 ], the Shrödinger equation with non-linear damping and harmonic potential is treated, precisely global well-posedness and decay are discussed. When \gamma =0, the problem ( 1.1) is a coupled non-linear system. … green fade to white background