Results 31 to 40 of about 66 (60)

Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening

Advances in Nonlinear Analysis
The Maxwell-Bloch system of equations with inhomogeneous broadening is studied, and the local and global well-posedness of the corresponding initial-boundary value problem is established by taking advantage of the integrability of the system and making ...
Biondini Gino, Prinari Barbara, Zhang Zechuan   +2 more
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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

LONG TIME BEHAVIOR OF THE SOLUTIONS OF NLW ON THE $d$-DIMENSIONAL TORUS

Forum of Mathematics, Sigma, 2020
We consider the nonlinear wave equation (NLW) on the $d$-dimensional torus $\mathbb{T}^{d}$ with a smooth nonlinearity of order at least 2 at the origin. We prove that, for almost any mass, small and smooth solutions of high Sobolev indices are stable up
JOACKIM BERNIER, ERWAN FAOU, BENOÎT GRÉBERT   +2 more
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Resonance-based schemes for dispersive equations via decorated trees

Forum of Mathematics, Pi, 2022
We introduce a numerical framework for dispersive equations embedding their underlying resonance structure into the discretisation. This will allow us to resolve the nonlinear oscillations of the partial differential equation (PDE) and to approximate ...
Yvain Bruned, Katharina Schratz
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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
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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
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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
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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
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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