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Perturbation Analysis of the Nonlinear Matrix Equation [PDF]
Abstract and Applied Analysis, 2013 Consider the nonlinear matrix equation with . Two perturbation bounds and the backward error of an approximate solution to the equation are derived. Explicit expressions of the condition number for the equation are obtained.
Jing Li
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On the Positive Definite Solutions of a Nonlinear Matrix Equation [PDF]
Journal of Applied Mathematics, 2013 The positive definite solutions of the nonlinear matrix equation are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived.
Panpan Liu, Shugong Zhang, Qingchun Li
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Comment on “Perturbation Analysis of the Nonlinear Matrix Equation ” [PDF]
Abstract and Applied Analysis, 2013 We show that the perturbation estimate for the matrix equation due to J. Li, is wrong. Our discussion is supported by a counterexample.
Maher Berzig, Erdal Karapınar
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Integration of the Matrix Nonlinear Schr¨odinger Equation with a Source
Известия Иркутского государственного университета: Серия "Математика", 2021 This paper is concerned with studying the matrix nonlinear Schr¨odinger equation with a self-consistent source. The source consists of the combination of the eigenfunctions of the corresponding spectral problem for the matrix Zakharov-Shabat system which
G.U. Urazboev +2 more
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On $\Psi$-stability of nonlinear Lyapunov matrix differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2009 We prove necessary and sufficient conditions for $\Psi -$ (uniform) stability of the trivial solution of a nonlinear Lyapunov matrix differential equation.
Aurel Diamandescu
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On the Propagation Model of Two-Component Nonlinear Optical Waves
Axioms, 2023 Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated.
Aleksandr O. Smirnov, Eugeni A. Frolov
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Numerical differential continuation approach for systems of nonlinear equations with singular Jacobian [PDF]
AUT Journal of Mathematics and Computing, 2022 It is well known that, one of the useful and rapid methods for a nonlinear system of algebraic equations is Newton’s method. Newton’s method has at least quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution ...
Mohammad Ali Mehrpouya
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The matrix nonlinear Schrödinger equation with a potential
Journal de Mathématiques Pures et Appliquées, 2023 This paper is devoted to the study of the large-time asymptotics of the small solutions to the matrix nonlinear Schrödinger equation with a potential on the half-line and with general selfadjoint boundary condition, and on the line with a potential and a general point interaction, in the whole supercritical regime. We prove that the small solutions are
Naumkin, Ivan, Weder, Ricardo
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Barycentric Rational Collocation Method for Nonlinear Heat Conduction Equation
Journal of Applied Mathematics, 2022 Nonlinear heat equation solved by the barycentric rational collocation method (BRCM) is presented. Direct linearization method and Newton linearization method are presented to transform the nonlinear heat conduction equation into linear equations.
Jin Li
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Advances in Difference Equations, 2021 In this article, we introduce a class of stochastic matrix control functions to stabilize a nonlinear fractional Volterra integro-differential equation with Ψ-Hilfer fractional derivative.
Reza Chaharpashlou, Reza Saadati
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