LAUSR

About LAUSR
Donate
Contact Us

Follow us:

You are not signed in:

Sign Up!


   Articles with "schr dinger" as a keyword



Photo by saadahmad_umn from unsplash

Strichartz estimates for non‐degenerate Schrödinger equations

Sign Up to like & get
recommendations! Published in 2020 at "Mathematische Nachrichten"

DOI: 10.1002/mana.201800148

Abstract: We consider the Schrödinger equation with a non‐degenerate metric on the Euclidean space. We study local in time Strichartz estimates for the Schrödinger equation without loss of derivatives including the endpoint case. In contrast to… read more here.

Keywords: dinger equation; strichartz estimates; estimates non; non degenerate ... See more keywords
Photo by daveballew from unsplash

A note on the Schrödinger smoothing effect

Sign Up to like & get
recommendations! Published in 2019 at "Mathematische Nachrichten"

DOI: 10.1002/mana.201800502

Abstract: The Kato–Yajima smoothing estimate is a smoothing weighted L2 estimate with a singular power weight for the Schrödinger propagator. The weight has been generalized relatively recently to Morrey–Campanato weights. In this paper we make this… read more here.

Keywords: schr; note schr; dinger smoothing; schr dinger ... See more keywords
Photo by shotsbywolf from unsplash

Global dynamics for a class of inhomogeneous nonlinear Schrödinger equations with potential

Sign Up to like & get
recommendations! 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
Photo by jawis from unsplash

Characteristics of rogue waves on a soliton background in a coupled nonlinear Schrödinger equation

Sign Up to like & get
recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.5532

Abstract: In this paper, a coupled nonlinear Schrödinger (CNLS) equation, which can describe evolution of localized waves in a two‐mode nonlinear fiber, is under investigation. By using the Darboux‐dressing transformation, the new localized wave solutions of… read more here.

Keywords: coupled nonlinear; waves soliton; nonlinear schr; rogue waves ... See more keywords
Photo by mael_balland from unsplash

Schrödinger‐Poisson system with Hardy‐Littlewood‐Sobolev critical exponent

Sign Up to like & get
recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.5694

Abstract: In this paper, we consider the following Schrödinger‐Poisson system: −Δu+λϕ|u|2α∗−2u=∫R3|u|2β∗|x−y|3−βdy|u|2β∗−2u,inR3,(−Δ)α2ϕ=Aα−1|u|2α∗,inR3, where parameters α,β∈(0,3),λ>0, Aα=Γ(3−α2)2απ32Γ(α2) , 2α∗=3+α , and 2β∗=3+β are the Hardy‐Littlewood‐Sobolev critical exponents. For α0, we prove the existence of nonnegative groundstate solution to… read more here.

Keywords: dinger poisson; system; hardy littlewood; littlewood sobolev ... See more keywords
Photo by saadahmad_umn from unsplash

Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity

Sign Up to like & get
recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.5827

Abstract: The main aim of this article is to present some new exact solutions of the resonant nonlinear Schrödinger equation. These solutions are derived by using the generated exponential rational function method (GERFM). The kink‐type, bright,… read more here.

Keywords: dinger equation; schr dinger; nonlinear schr;
Photo by mael_balland from unsplash

Nontrivial solutions for the fractional Schrödinger‐Poisson system with subcritical or critical nonlinearities

Sign Up to like & get
recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.6019

Abstract: In this paper, we are concerned with a class of fractional Schrödinger‐Poisson system involving subcritical or critical nonlinearities. By using the Nehari manifold and variational methods, we obtain the existence and multiplicity of nontrivial solutions. read more here.

Keywords: dinger poisson; fractional schr; critical nonlinearities; poisson system ... See more keywords
Photo by mael_balland from unsplash

Existence and multiplicity of normalized solutions for a class of Schrödinger‐Poisson equations with general nonlinearities

Sign Up to like & get
recommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.6140

Abstract: In this paper, we study the existence and multiplicity of standing waves with prescribed L2 ‐norm Schrödinger‐Poisson equations with general nonlinearities in R3 : i∂tψ+Δψ−κ(|x|−1*|φ|2)ψ+f(ψ)=0, where κ>0 and f is superlinear and satisfies the monotonicity… read more here.

Keywords: dinger poisson; schr dinger; existence multiplicity; equations general ... See more keywords
Photo by mael_balland from unsplash

Multibump solutions for nonlinear Schrödinger‐Poisson systems

Sign Up to like & get
recommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.6211

Abstract: In this paper, we study the following Schrödinger‐Poisson equations: −ε2Δu+V(x)u+K(x)ϕu=|u|p−2u,x∈R3,−ε2Δϕ=K(x)u2,x∈R3, where p∈(4,6) , ε>0 is a parameter and V and K satisfy the critical frequency conditions. By using variational methods and penalization arguments, we show… read more here.

Keywords: dinger poisson; schr dinger; solutions nonlinear; multibump solutions ... See more keywords
Photo by mael_balland from unsplash

Existence and limiting behavior of minimizers for attractive Schrödinger‐Poisson systems with periodic potentials

Sign Up to like & get
recommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.6232

Abstract: We study the constrained minimizing problem of the energy functional related to attractive Schrödinger‐Poisson systems with periodic potentials: I(m)=infE(ϕ):ϕ∈H1(R3),‖ϕ‖L22=m, where E(ϕ):=12∫R3|∇ϕ(x)|2dx+12∫R3V(x)|ϕ(x)|2dx−14∬R3×R3|ϕ(x)|2|ϕ(y)|2|x−y|dxdy−1α+2∫R3|ϕ(x)|α+2dx, with m>0 , α>0 , and V is a continuous periodic potential. We first… read more here.

Keywords: poisson systems; dinger poisson; attractive schr; systems periodic ... See more keywords
Photo by kellysikkema from unsplash

A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations

Sign Up to like & get
recommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.6709

Abstract: In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer… read more here.

Keywords: schr dinger; type equations; fractal dimension; nonlinear schr ... See more keywords