Global dynamics for a class of inhomogeneous nonlinear Schrödinger equations with potential
Sign Up to like & getrecommendations! Published in 2021 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201900427
Abstract: We consider a class of L2‐supercritical inhomogeneous nonlinear Schrödinger equations with potential in three dimensions. In the focusing case, using a recent method of Dodson and Murphy, we first study the energy scattering below the… read more here.
Keywords: class; equations potential; nonlinear schr; inhomogeneous nonlinear ... See more keywords
Strong instability of solitary waves for inhomogeneous nonlinear Schrödinger equations
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7731
Abstract: This paper studies the inhomogeneous nonlinear Schrödinger equations, which may model the propagation of laser beams in nonlinear optics. Using the cross‐constrained variational method, a sharp condition for global existence is derived. Then, by solving… read more here.
Keywords: instability solitary; nonlinear schr; strong instability; inhomogeneous nonlinear ... See more keywords
Scattering for Stochastic Nonlinear Schrödinger Equations
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03429-0
Abstract: We study the scattering behavior of global solutions to stochastic nonlinear Schrödinger equations with linear multiplicative noise. In the case where the quadratic variation of the noise is globally finite and the nonlinearity is defocusing,… read more here.
Keywords: stochastic nonlinear; nonlinear schr; schr dinger; dinger equations ... See more keywords
Global Well-Posedness and Analytic Smoothing Effect for the Dissipative Nonlinear Schrödinger Equations
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-018-9709-4
Abstract: We study the global Cauchy problem for the nonlinear Schrödinger equations in the Sobolev space of fractional order. In particular, we show the global well-posedness and the analytic smoothing effect for global solutions to a… read more here.
Keywords: nonlinear schr; dinger equations; global well; well posedness ... See more keywords
The locally extrapolated exponential splitting scheme for multi-dimensional nonlinear space-fractional Schrödinger equations
Sign Up to like & getrecommendations! Published in 2017 at "Numerical Algorithms"
DOI: 10.1007/s11075-017-0291-3
Abstract: An efficient local extrapolation of the exponential operator splitting scheme is introduced to solve the multi-dimensional space-fractional nonlinear Schrödinger equations. Stability of the scheme is examined by investigating its amplification factor and by plotting the… read more here.
Keywords: scheme; schr dinger; dinger equations; space fractional ... See more keywords
Standing waves for quasilinear Schrödinger equations with indefinite potentials
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2018.05.024
Abstract: Abstract We consider quasilinear Schrodinger equations in R N of the form − Δ u + V ( x ) u − u Δ ( u 2 ) = g ( u ) , where… read more here.
Keywords: dinger equations; waves quasilinear; equations indefinite; quasilinear schr ... See more keywords
Nonlinear Schrödinger equations with exceptional potentials
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2018.06.016
Abstract: We consider the cubic nonlinear Schrodinger equation with an exceptional potential. We obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions. We… read more here.
Keywords: nonlinear schr; dinger equations; time; exceptional potentials ... See more keywords
Finite time extinction for a class of damped Schrödinger equations with a singular saturated nonlinearity
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2021.11.010
Abstract: We present some sharper finite extinction time results for solutions of a class of damped nonlinear Schrödinger equations when the nonlinear damping term corresponds to the limit cases of some “saturating non-Kerr law” F (|u|)u… read more here.
Keywords: dinger equations; class damped; extinction; time ... See more keywords
Schrödinger equations with van der Waals type potentials
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.10.075
Abstract: Abstract In this paper, we consider the following elliptic problem: (0.1) − Δ u + V ( x ) u + λ ( κ α ⁎ | u | p ) | u | p… read more here.
Keywords: schr dinger; equations van; van der; der waals ... See more keywords
Infinitely many solutions for a class of quasilinear Schrödinger equations involving sign-changing weight functions
Sign Up to like & getrecommendations! Published in 2019 at "Applicable Analysis"
DOI: 10.1080/00036811.2017.1422726
Abstract: ABSTRACT Using a change of variables and the constrained critical point theory, we first prove the existence and multiplicity of solutions for a class of quasilinear Schrödinger equations. Next, we consider a quasilinear equation related… read more here.
Keywords: dinger equations; class quasilinear; solutions class; sign changing ... See more keywords
Concentrating ground state solutions for quasilinear Schrödinger equations with steep potential well
Sign Up to like & getrecommendations! Published in 2019 at "Applicable Analysis"
DOI: 10.1080/00036811.2019.1707814
Abstract: We are concerned with the following quasilinear Schrödinger equations (1) where , are parameters, V and f are nonnegative continuous functions, is a positive bounded function. By using variational methods, we study the existence of… read more here.
Keywords: dinger equations; state solutions; quasilinear schr; ground state ... See more keywords