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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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Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians
Advanced Nonlinear Studies, 2022 The purpose of this article is to establish sharp conditions for the existence of normalized solutions to a class of scalar field equations involving mixed fractional Laplacians with different orders.
Luo Tingjian, Hajaiej Hichem
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Optical vortices in dispersive nonlinear Kerr‐type media
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 18, Page 949-967, 2004., 2004 The applied method of slowly varying amplitudes gives us the possibility to reduce the nonlinear vector integrodifferential wave equation of the electrical and magnetic vector fields to the amplitude vector nonlinear differential equations. Using this approximation, different orders of dispersion of the linear and nonlinear susceptibility can be ...
Lubomir M. Kovachev
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