Results 91 to 100 of about 3,496 (115)

Long-time asymptotic behavior for the Hermitian symmetric space derivative nonlinear Schrödinger equation

Advanced Nonlinear Studies
Resorting to the spectral analysis of the 4 × 4 matrix spectral problem, we construct a 4 × 4 matrix Riemann–Hilbert problem to solve the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation.
Chen Mingming, Geng Xianguo, Liu Huan
doaj   +1 more source

Sharp well-posedness for the cubic NLS and mKdV in $H^s({{\mathbb {R}}})$

Forum of Mathematics, Pi
We prove that the cubic nonlinear Schrödinger equation (both focusing and defocusing) is globally well-posed in $H^s({{\mathbb {R}}})$ for any regularity $s>-\frac 12$ .
Benjamin Harrop-Griffiths, Rowan Killip, Monica Vişan   +2 more
doaj   +1 more source

The elliptic sinh-Gordon equation in a semi-strip

Advances in Nonlinear Analysis, 2017
We study the elliptic sinh-Gordon equation posed in a semi-strip by applying the so-called Fokas method, a generalization of the inverse scattering transform for boundary value problems.
Hwang Guenbo
doaj   +1 more source

Multiple positive solutions for a class of concave-convex Schrödinger-Poisson-Slater equations with critical exponent

Advances in Nonlinear Analysis
In this article, we consider the multiplicity of positive solutions for a static Schrödinger-Poisson-Slater equation of the type −Δu+u2∗1∣4πx∣u=μf(x)∣u∣p−2u+g(x)∣u∣4uinR3,-\Delta u+\left({u}^{2}\ast \frac{1}{| 4\pi x| }\right)u=\mu f\left(x){| u| }^{p-2 ...
Zheng Tian-Tian, Lei Chun-Yu, Liao Jia-Feng   +2 more
doaj   +1 more source

Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity

Advances in Nonlinear Analysis, 2018
This paper is concerned with the following Kirchhoff-type problem with convolution nonlinearity:
Chen Sitong, Zhang Binlin, Tang Xianhua
doaj   +1 more source

Bootstrapped Morawetz Estimates And Resonant Decomposition For Low Regularity Global Solutions Of Cubic NLS On R^{2} [PDF]

arXiv, 2008
We prove global well-posedness for the L^{2}-critical cubic defocusing nonlinear Schr\"odinger equation on R^{2} with data u_{0} \in H^{s}(R^{2}) for s > {1/3}.
arxiv  

Nodal solutions for a zero-mass Chern-Simons-Schrödinger equation

Advances in Nonlinear Analysis
This study deals with the existence of nodal solutions for the following gauged nonlinear Schrödinger equation with zero mass: −Δu+hu2(∣x∣)∣x∣2+∫∣x∣+∞hu(s)su2(s)dsu=∣u∣p−2u,x∈R2,-\Delta u+\left(\frac{{h}_{u}^{2}\left(| x| )}{{| x| }^{2}}+\underset{| x| }{
Deng Yinbin, Liu Chenchen, Yang Xian
doaj   +1 more source

The new solitary wave structures for the (2 + 1)-dimensional time-fractional Schrodinger equation and the space-time nonlinear conformable fractional Bogoyavlenskii equations

Alexandria Engineering Journal, 2020
The present paper employs the space-time fractional nonlinear Bogoyavlenskii equation and Schrodinger equation. We perform a new method to take some new solitary wave phenomena for each equation.
Md Nur Alam, Cemil Tunç
doaj  

A note on coupled nonlinear Schrödinger systems under the effect of general nonlinearities [PDF]

arXiv, 2009
We prove the existence of non-trivial solutions to a system of coupled, nonlinear, Schroedinger equations with general nonlinearity.
arxiv  

Mixed norm estimates of Schrödinger waves and their applications [PDF]

arXiv, 2009
In this paper we establish mixed norm estimates of interactive Schr\"{o}dinger waves and apply them to study smoothing properties and global well-posedness of the nonlinear Schr\"{o}dinger equations with mass critical nonlinearity.
arxiv