We consider the Euler equations describing nonlinear waves on the free surface of a twodimensional inviscid, irrotational fluid layer of finite depth. For large surface tension, Bond number larger than 1=3, and Froude number close to 1, the system possesses a one-parameter family of small-amplitude, traveling solitary wave solutions. We show that these solitary waves are spectrally stable with ...

In this paper we prove the existence of a solution to a nonlinear Schrödinger–Poisson eigenvalue problem in dimension less than 3. Our proof is based on a global approach to the determination of eigenvalues and eigenfunctions which allows us to characterize the complete sequence of eigenvalues and eigenfunctions at once, via a variational approach, and thus differs from the usual and less gener...

In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...

Asymptotic dynamics of ordinary differential equations (ODEs) are commonly understood by looking at eigenvalues of a matrix, and transient dynamics can be bounded above and below by considering the corresponding pseudospectra. While asymptotics for other classes of differential equations have been studied using eigenvalues of a (nonlinear) matrix-valued function, there are no analogous pseudosp...

In this paper we systematically derive a linear model for an n bus m machine system with nonlinear voltage dependent loads at the network buses. The model is versatile and can be used to study diierent phenomena such as steady-state stability, voltage stability, etc. In addition to obtaining the system A matrix, we also obtain a transfer function between load voltages/angles and real/reactive p...

This work is devoted to the numerical approximation of the solutions to the system of conservation laws which arises in the modeling of two-phase flows in pipelines. The PDEs are closed by two highly nonlinear algebraic relations, namely, a pressure law and a hydrodynamic law. We have previously proposed an explicit relaxation scheme which allows us to cope with these nonlinearities. But the sy...

The stability of the equilibria of time-invariant nonlinear dynamical systems with discrete time scale is investigated. We present an elementary proof showing that in the case of a stable equilibrium and continuously di€erentiable state transition function, all eigenvalues of the Jacobian computed at the equilibrium must be inside or on the unit circle. We also demonstrate via numerical example...

It is well known that the nonlinear PDE describing the dynamics of a hydrodynamically unstable planar flame front admits exact pole solutions as equilibrium states. Such a solution corresponds to a steadily propagating cusp-like structure commonly observed in experiments. In this work we investigate the linear stability of these equilibrium states—the steady coalescent pole solutions. In previo...

In this paper we systematically derive a linear model for a n bus m machine system with nonlinear voltage dependent loads at the network buses. The model is versatile and can be used to study diierent phenomena such as steady state stability or voltage collapse. In addition to obtaining the system A matrix, we also obtain a transfer function between load voltages/angles and real/reactive powers...