We construct a gauge theory based on nonlinear Lie algebras, which is an extension of the usual gauge theory based on Lie algebras. It is a new approach to generalization of the gauge theory. The two-dimensional gravity is derived from nonlinear Poincaré algebra, which is the new Yang-Mills like formulation of the gravitational theory. As typical examples, we investigate R2 gravity with dynamic...

Extensions of sliding-mode adaptive observer are presented for state reconstruction of nonlinear systems with uncertainty having unknown bounds. The observer uses nonlinear gains that are smoothened versions of classical sliding-mode gains and they are continuously updated to guarantee a globally stable observation error. This observer is applied to Chua’s circuit in a chaotic synchronization s...

In this article, we propose a generalization of the theory of di usion approximation for random ODE to a nonlinear system of random Schrödinger equations. This system arises in the study of pulse propagation in randomly birefringent optical bers. We rst show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Garnier-Marty [16, 20], where a ...

In this article, we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schrödinger equations. This system arises in the study of pulse propagation in randomly birefringent optical fibers. We first show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Garnier-Marty [16, 20], whe...

∗ Division of Automatic Control Department of Electrical Engineering, Linköpings universitet, SE-581 83 Linköping, Sweden ∗∗ Department of Mechanical Science and Engineering, Nagoya University, Japan Abstract: In this work, a computational method to compute balanced realizations for nonlinear differential-algebraic equation systems is derived. The work is a generalization of an earlier work for...

We introduced a nonlinear shot-noise model, a natural generalization of the "classic" shot-noise model, which differs markedly from the existing linear shot-noise models. This model produces a wide spectrum of stationary noise processes. Because of its intrinsic nonlinearity, the model's resulting noise processes are capable of displaying a rich variety of both amplitudal and temporal statistic...

We present a generalization of the Multiscale Enrichment based on Partition of Unity (MEPU) formulation originally reported in [1] to account for boundary layers, nonperiodic fields and nonlinear systems. MEPU is aimed at extending the range of applicability of the mathematical homogenization theory to nonlinear nonperiodic systems with inseparable fine and coarse scales. Performance studies fo...

A theory of nonlinear response is developed for driving fields of arbitrary magnitude. Exact and usable expressions are provided for electrical and thermal mobility, and related transport coefficients, in terms of correlation functions of the system. A generalization into the nonlinear domain is provided of the WiedemannFranz law connecting electrical and thermal response and of the Einstein re...

A nonlinear generalization of the Fluctuation-Dissipation Theorem (FDT) for the n-point Green functions and the amputated 1PI vertex functions at finite temperature is derived in the framework of the Closed Time Path formalism. We verify that this generalized FDT coincides with known results for n = 2 and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuatio...

The integrability of a system of two symmetrically coupled higherorder nonlinear Schrödinger equations is tested by means of the singularity analysis. It is proven that the system passes the Painlevé test for integrability only in ten distinct cases, of which two are new. For one of the new cases, a Lax pair and a multi-field generalization are obtained; for the other one, the equations of the ...