Results 51 to 60 of about 3,496 (115)

Ground state solutions for magnetic Schrödinger equations with polynomial growth

Advances in Nonlinear Analysis
In this article, we investigate the following nonlinear magnetic Schrödinger equations: (−i∇+A(x))2u+V(x)u=f1(x,∣v∣2)v,(−i∇+A(x))2v+V(x)v=f2(x,∣u∣2)u,\left\{\begin{array}{l}{\left(-i\nabla +A\left(x))}^{2}u+V\left(x)u={f}_{1}\left(x,{| v| }^{2})v ...
Wu Yan, Chen Peng
doaj   +1 more source

Low regularity conservation laws for Fokas-Lenells equation and Camassa-Holm equation

Advances in Nonlinear Analysis
In this article, we mainly prove low regularity conservation laws for the Fokas-Lenells equation in Besov spaces with small initial data both on the line and on the circle. We develop a new technique in Fourier analysis and complex analysis to obtain the
Shan Minjie, Chen Mingjuan, Lu Yufeng, Wang Jing   +3 more
doaj   +1 more source

A note on coupled nonlinear Schrödinger equations

Advances in Nonlinear Analysis, 2014
We investigate the initial value problem for some coupled nonlinear Schrödinger equations in two space dimensions with exponential growth. We prove global well-posedness and scattering in the defocusing case. In the focusing sign, existence of non-global
Saanouni Tarek
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Improved results on planar Klein-Gordon-Maxwell system with critical exponential growth

Advances in Nonlinear Analysis
This work is concerned with the following Klein-Gordon-Maxwell system: −Δu+V(x)u−(2ω+ϕ)ϕu=f(u),x∈R2,Δϕ=(ω+ϕ)u2,x∈R2,\left\{\begin{array}{ll}-\Delta u+V\left(x)u-\left(2\omega +\phi )\phi u=f\left(u),\hspace{1.0em}& x\in {{\mathbb{R}}}^{2},\\ \Delta \phi =
Wen Lixi, Jin Peng
doaj   +1 more source

Newton's law for a trajectory of concentration of solutions to nonlinear Schrodinger equation [PDF]

arXiv, 2013
One of important problems in mathematical physics concerns derivation of point dynamics from field equations. The most common approach to this problem is based on WKB method. Here we describe a different method based on the concept of trajectory of concentration.
arxiv  

Blow-up of solutions to cubic nonlinear Schrödinger equations with defect: The radial case

Advances in Nonlinear Analysis, 2017
In this article we investigate both numerically and theoretically the influence of a defect on the blow-up of radial solutions to a cubic NLS equation in dimension 2.
Goubet Olivier, Hamraoui Emna
doaj   +1 more source

Mass Concentration and Asymptotic Uniqueness of Ground State for 3-Component BEC with External Potential in ℝ2

Advanced Nonlinear Studies, 2021
We investigate the ground states of 3-component Bose–Einstein condensates with harmonic-like trapping potentials in ℝ2{\mathbb{R}^{2}}, where the intra-component interactions μi{\mu_{i}} and the inter-component interactions βi⁢j=βj⁢i{\beta_{ij}=\beta_{ji}
Kong Yuzhen, Wang Qingxuan, Zhao Dun
doaj   +1 more source

On the Schrödinger flows [PDF]

Proceedings of the ICM, Beijing 2002, vol. 2, 283--292, 2003
We present some recent results on the existence of solutions of the Schr\"odinger flows, and pose some problems for further research.
arxiv  

Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations

, 2015
We study the Gerdjikov-Ivanov (GI) equation and present a standard Darboux transformation for it. The solution is given in terms of quasideterminants.
Yilmaz, Halis
core   +1 more source

Uniqueness of the modified Schroedinger map in H^{3/4+e}(R^2) [PDF]

arXiv, 2005
We establish local well-posedness of the modified Schroedinger map in H^s, s>3/4.
arxiv