Results 71 to 80 of about 34,063 (197)
Selection of the ground state for nonlinear schrödinger equations [PDF]
, 2003 We prove for a class of nonlinear Schrodinger systems (NLS) having two nonlinear bound states that the (generic) large time behavior is characterized by decay of the excited state, asymptotic approach to the nonlinear ground state and dispersive ...
A. Soffer, M. Weinstein, M. Weinstein
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.We investigate the Cauchy problem for the fourth‐order Schrödinger equation with quadratic nonlinearities involving second‐order derivatives: uxxu, uxxū, (ux)2, uūxx, and |ux|2, where u = u(x, t) is a complex‐valued function defined on R×R. The flow map of this Cauchy problem with the nonlinear terms uxxu or uxxū fails to be C2 differentiable at zero ...
Long Xiao, Ting Chen, Xian-Ming Gu
wiley +1 more source
MathematicsThe nonlinear Schrödinger (NLS) equation stands as a cornerstone model for exploring the intricate behavior of weakly nonlinear, quasi-monochromatic wave packets in dispersive media. Its reach extends across diverse physical domains, from surface gravity
Natanael Karjanto
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Advances in Difference Equations, 2021 Ablowitz–Kaup–Newell–Segur (AKNS) linear spectral problem gives birth to many important nonlinear mathematical physics equations including nonlocal ones.
Bo Xu, Yufeng Zhang, Sheng Zhang
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Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement
, 2015 We consider the three-dimensional time-dependent Gross-Pitaevskii equation arising in the description of rotating Bose-Einstein condensates and study the corresponding scaling limit of strongly anisotropic confinement potentials.
Mehats, Florian, Sparber, Christof
core +3 more sources
An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing Nonlinearity [PDF]
SIAM Journal on Numerical Analysis, 2003 This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrodinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant.
W. Bao, D. Jaksch
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Quasi‐invariance of Gaussian measures for the 3d$3d$ energy critical nonlinear Schrödinger equation
Communications on Pure and Applied Mathematics, Volume 78, Issue 12, Page 2305-2353, December 2025.Abstract We consider the 3d$3d$ energy critical nonlinear Schrödinger equation with data distributed according to the Gaussian measure with covariance operator (1−Δ)−s$(1-\Delta)^{-s}$, where Δ$\Delta$ is the Laplace operator and s$s$ is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple
Chenmin Sun, Nikolay Tzvetkov
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International Journal of Differential EquationsThe mathematical models of problems that arise in many branches of science are nonlinear equations of evolution (NLEE). For this reason, NLEE have served as a language in formulating many engineering and scientific problems.
Murat Koparan
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Rogue waves and periodic solutions of a nonlocal nonlinear Schrödinger model
Physical Review Research, 2020 In the present paper, a nonlocal nonlinear Schrödinger (NLS) model is studied by means of a recent technique that identifies solutions of partial differential equations by considering them as fixed points in space-time.
C. B. Ward +3 more
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Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity [PDF]
, 2009 For a large class of nonlinear Schrodinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity, we prove the existence of nontrivial finite energy traveling waves moving with speed c in any space dimension N?3 ...
Mihai Marics
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