Results 61 to 70 of about 1,785 (116)

Blow-up criteria for the inhomogeneous nonlinear Schrödinger equation

, 2014
In this paper, using the variational characteristic of the virial identity and a new estimate of the kinetic energy, we obtain a new sufficient condition for the existence of blow-up solutions.MSC:35Q55, 35B44.
Han Yang, Shihui Zhu
semanticscholar   +1 more source

On the instability for the cubic nonlinear Schrodinger equation

, 2007
We study the flow map associated to the cubic Schrodinger equation in space dimension at least three.
Burq, Carles, Cazenave, Grenier, Rémi Carles, Sone   +5 more
core   +1 more source

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

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   +1 more source

Closed Form Solutions of Integrable Nonlinear Evolution Equations [PDF]

, 2012
2010 Mathematics Subject Classification: 35Q55.In this article we obtain closed form solutions of integrable nonlinear evolution equations associated with the nonsymmetricmatrix Zakharov- Shabat system by means of the inverse scattering transform.
van der Mee, Cornelis
core   +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

On the Cauchy problem for Gross-Pitaevskii hierarchies

, 2011
The purpose of this paper is to investigate the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n,$ $n \geq 1.$ We prove local existence and uniqueness of solutions in certain Sobolev type spaces $\mathrm{H}^{
Chuangye Liu, Erdös L., Pitaevskii L. P., Zeqian Chen   +3 more
core   +1 more source

Existence of a Positive Solution to a Nonlinear Scalar Field Equation with Zero Mass at Infinity

Advanced Nonlinear Studies, 2018
We establish the existence of a positive solution to the ...
Clapp Mónica, Maia Liliane A.
doaj   +1 more source

Limit profiles and the existence of bound-states in exterior domains for fractional Choquard equations with critical exponent

Advances in Nonlinear Analysis
This article is devoted to studying the existence of positive solutions to the following fractional Choquard equation: (−Δ)su+u=∫Ω∣u(y)∣p∣x−y∣N−αdy∣u∣p−2u+ε∫Ω∣u(y)∣2α,s*∣x−y∣N−αdy∣u∣2α,s*−2u,inΩ,u=0,onRN\Ω,\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+u=
Ye Fumei, Yu Shubin, Tang Chun-Lei
doaj   +1 more source

High-energy solutions for coupled Schrödinger systems with critical growth and lack of compactness

Advances in Nonlinear Analysis
This article deals with the existence of high-energy positive solutions for the following coupled Schrödinger system with critical exponent: −Δu+V1(x)u=μ1u3+βuv2,x∈Ω,−Δv+V2(x)v=βu2v+μ2v3,x∈Ω,u,v∈D01,2(Ω)\left\{\begin{array}{l}-\Delta u+{V}_{1}\left(x)u={\
Guan Wen, Wang Da-Bin, Xie Huafei
doaj   +1 more source