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Advances in Nonlinear Analysis, 2021 In this paper we are concerned with the existence, nonexistence and bifurcation of nontrivial solution of the nonlinear Schrödinger-Korteweg-de Vries type system(NLS-NLS-KdV).
Geng Qiuping, Wang Jun, Yang Jing
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Blow-up solutions with minimal mass for nonlinear Schrödinger equation with variable potential
Advances in Nonlinear Analysis, 2021 This paper studies the mass-critical variable coefficient nonlinear Schrödinger equation. We first get the existence of the ground state by solving a minimization problem.
Pan Jingjing, Zhang Jian
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Well-Posedness and Uniform Decay Rates for a Nonlinear Damped Schrödinger-Type Equation
Advanced Nonlinear Studies, 2021 In this paper we study the existence as well as uniform decay rates of the energy associated with the nonlinear damped Schrödinger equation,
Cavalcanti Marcelo M. +1 more
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Open Mathematics, 2023 In this article, the coupled matrix nonlinear Schrödinger (NLS) type equations are gauge equivalent to the equation of Schrödinger flow from R1{{\mathbb{R}}}^{1} to complex Grassmannian manifold G˜n,k=GL(n,C)∕GL(k,C)×GL(n−k,C),{\widetilde{G}}_{n,k}={\rm ...
Zhong Shiping, Zhao Zehui, Wan Xinjie
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Existence of normalized solutions for the coupled elliptic system with quadratic nonlinearity
Advanced Nonlinear Studies, 2022 In the present paper, we study the existence of the normalized solutions for the following coupled elliptic system with quadratic nonlinearity −Δu−λ1u=μ1∣u∣u+βuvinRN,−Δv−λ2v=μ2∣v∣v+β2u2inRN,\left\{\begin{array}{ll}-\Delta u-{\lambda }_{1}u={\mu }_{1}| u|
Wang Jun, Wang Xuan, Wei Song
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Demonstratio Mathematica, 2022 In this article, we will prove the existence of infinitely many solutions for a class of quasilinear Schrödinger equations without assuming the 4-superlinear at infinity on the nonlinearity. We achieve our goal by using the Fountain theorem.
Khiddi Mustapha, Essafi Lakbir
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Fine Structure of Matrix Darboux-Toda Integrable Mapping [PDF]
, 1998 We show here that matrix Darboux-Toda transformation can be written as a product of a number of mappings. Each of these mappings is a symmetry of the matrix nonlinear Shrodinger system of integro-differential equations. We thus introduce a completely new
Leznov, A. N., Yuzbashyan, E. A.
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GLOBAL WELL-POSEDNESS OF THE PERIODIC CUBIC FOURTH ORDER NLS IN NEGATIVE SOBOLEV SPACES
Forum of Mathematics, Sigma, 2018 We consider the Cauchy problem for the cubic fourth order nonlinear Schrödinger equation (4NLS) on the circle. In particular, we prove global well-posedness of the renormalized 4NLS in negative Sobolev spaces $H^{s}(\mathbb{T})$
TADAHIRO OH, YUZHAO WANG
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J-Self-Adjointness of a Class of Dirac-Type Operators [PDF]
, 2004 In this note we prove that the maximally defined operator associated with a class of Dirac-type differential expressions M(Q) is J-self-adjoint with respect to a proper antilinear conjugation J under the general hypothesis that the entries of the matrix ...
Cascaval, Radu, Gesztesy, Fritz
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Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction
Advances in Nonlinear Analysis, 2021 In the present paperwe study the existence of nontrivial solutions of a class of static coupled nonlinear fractional Hartree type system. First, we use the direct moving plane methods to establish the maximum principle(Decay at infinity and Narrow region
Wang Jun
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