We suggest a generalized Lax pair on a Hermitian symmetric space to generate a new coupled higher-order nonlinear Schrödinger equation of a dual type which contains both bright and dark soliton equations depending on parameters in the Lax pair. Through the generalized ways of reduction and the scaling transformation for the coupled higher-order nonlinear Schrödinger equation, two integrable typ...

Introduction E IGENSTRUCTURE assignment algorithms are widely used to design control systems.Most of the available eigenstructure assignment algorithms assign all of the eigenvalues to the desired values.The eigenstructureassignmentalgorithmcan be dividedinto two groups, that is, the null space approach and Sylvester equation approach.The null spaceapproachis used to solvemode decoupling proble...

This chapter is about numerical methods for a particular type of equation expressed as a matrix equality. The Lyapunov equation is the most common problem in the class of problems called matrix equations. Other examples of matrix equations: Sylvester equation, Stein equation, Riccati equation. Definition 4.0.1. Consider two square matrices A, W ∈ Rn×n. The problem to find a square matrix X ∈ Rn...