Results 41 to 50 of about 1,721 (90)
Demonstratio MathematicaThis article is devoted to the study of the existence and nonexistence of normalized solutions for the following biharmonic Schrödinger equation with combined power-type ...
Liu Xiang, Huang Na, Lei Chunyu
doaj +1 more source
Advances in Nonlinear AnalysisThis paper examines the focusing nonlinear Schrödinger equation with an inverse-square potential in RN(N≥3) ${\mathbb{R}}^{N} \left(N\ge 3\right)$ , where the nonlinear exponent lies between the mass-critical and energy-subcritical regimes.
Lin Qiang, Chen Shaohua
doaj +1 more source
Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions
Advances in Nonlinear Analysis, 2019 In the present paper, we consider the following singularly perturbed problem:
Tang Xianhua, Chen Sitong
doaj +1 more source
On the Real Analyticity of the Scattering Operator for the Hartree Equation
, 2008 In this paper, we study the real analyticity of the scattering operator for the Hartree equation $ i\partial_tu=-\Delta u+u(V*|u|^2)$. To this end, we exploit interior and exterior cut-off in time and space, and combining with the compactness argument to
Miao, Changxing +2 more
core +1 more source
Self-similar blow-up solutions of the four-dimensional Schrödinger-Wave system
Advances in Nonlinear AnalysisThis article is primarily dedicated to the investigation of the initial value problem for the Schrödinger-wave system in dimension four. By employing self-similar transformations in conjunction with the Banach fixed-point theorem, we establish the ...
Hou Wenhe +3 more
doaj +1 more source
Unconditional uniqueness for the energy-critical nonlinear Schrödinger equation on $\mathbb {T}^{4}$
Forum of Mathematics, Pi, 2022 We consider the $\mathbb {T}^{4}$ cubic nonlinear Schrödinger equation (NLS), which is energy-critical. We study the unconditional uniqueness of solutions to the NLS via the cubic Gross–Pitaevskii hierarchy, an uncommon method for NLS analysis which is ...
Xuwen Chen, Justin Holmer
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
, 2008 In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an angular momentum rotational term in which the angular velocity is equal to the isotropic trapping frequency in the space $\Real^3 ...
Chengchun Hao +4 more
core +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 +3 more
core +1 more source
Ground state solutions for magnetic Schrödinger equations with polynomial growth
Advances in Nonlinear AnalysisIn 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