Ground State of N Coupled Nonlinear Schrodinger Equations in {\mathbb{R}}^n, n \leq 3
Tai-Chia Lin,Juncheng Wei +1 more
TLDR
In this paper, the existence and nonexistence of ground state solutions of N coupled nonlinear Schrodinger equations is established. But the sign of the coupling constants is not crucial for the existence of ground-state solutions.Abstract:
We establish some general theorems for the existence and nonexistence of ground state solutions of steady-state N coupled nonlinear Schrodinger equations. The sign of coupling constants β
ij
’s is crucial for the existence of ground state solutions. When all β
ij
’s are positive and the matrix Σ is positively definite, there exists a ground state solution which is radially symmetric. However, if all β
ij
’s are negative, or one of β
ij
’s is negative and the matrix Σ is positively definite, there is no ground state solution. Furthermore, we find a bound state solution which is non-radially symmetric when N=3.read more
Citations
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Least Energy Solitary Waves for a System of Nonlinear Schrödinger Equations in \({\mathbb{R}^n}\)
Boyan Sirakov,Boyan Sirakov +1 more
TL;DR: In this paper, the existence of least energy standing waves (solitons) in higher dimensions was studied and conditions on the parameters of the system under which it possesses a solution with least energy among all multi-component solutions were given.
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Standing waves of some coupled nonlinear Schrödinger equations
TL;DR: In this paper, the existence of bound and ground states for nonlinear Schrodinger equations is proved provided the coupling parameter is small and large, respectively, for a class of nonlinear systems of Schroffinger equations.
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A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system
TL;DR: In this paper, the local and global bifurcation structure of positive solutions of nonlinear elliptic Schrodinger type equations was studied in nonlinear optics and Hartree-Fock theory for a double condensate.
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A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system
TL;DR: In this article, it was shown that β ≥ − μ 1 μ 2 is critical for the existence of a priori bounds for the Bose-Einstein double condensates of nonlinear elliptic systems.
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Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations
Juncheng Wei,Tobias Weth +1 more
TL;DR: In this paper, it was shown that the nonlinear elliptic system admits a radially symmetric solution (uβ, vβ) such that uβ − vβ changes sign precisely k times in the radial variable.
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