We prove the linear and nonlinear instability of the line solitary water waves with respect to transverse perturbations.

We investigate coupled stochastic differential equations governing N nonnegative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires a set of fluctuating variables to be nonnegative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of ...

We study a robust optimal stopping problem with respect to a set P of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from P. We show that the upper Snell envelope Z of the reward process Y is a supermartin...

When the range of the derivative of the nonlinearity contains the rst k eigenvalues of the linear part and a certain parameter is large, we establish the existence of 2k radial solutions to a semilinear boundary value problem. This proves the Lazer McKenna conjecture for radial solutions. Our results supplement those in 5], where the existence of k + 1 solutions was proven.

A combined model of the Kerr spinning particle and superparticle is considered. The structure of the Kerr geometry is presented in a complex form as being created by a complex source. A natural supergeneralization of this construction is obtained corresponding to a complex " supersource ". Peforming a supershift to the Kerr and Kerr-Sen solutions we obtain metrics of supergravity black holes wi...

Rate and magnitude control limitations are often responsible for the apparition of undesired limit-cycles in the resulting nonlinear closed-loop system. Based on the wellknown describing function approach, it is shown in this paper that such limit cycles can be avoided as soon as H∞ constraints are simultaneously satisfied by appropriately chosen linear interconnections. This result is then use...

The boundary layer flow of a second grade fluid over a permeable stretching surface with arbitrary velocity and appropriatewall transpiration is investigated. The fluid is electrically conducting in the presence of a constant applied magnetic field. An exact solution to the nonlinear flow problem is presented. © 2011 Elsevier Ltd. All rights reserved.

Magnetic reconnection based on the resistive and Hall MHD equations are reviewed. It is found from both theory and simulation that the impulsive reconnection can be achieved in the resistive and Hall MHD by imposing suitable boundary conditions. All results from resistive and Hall MHD indicate that reconnection processes contain two phases: slow growth phase and impulsive phase, and between the...

In this paper we propose a strategy to obtain the solutions of a scalar equation f (x) = 0 through solving an associated system of two equations. In this way, the solutions of the associated system lying on the identity line provide solutions of the given equation. In most cases, the associated system cannot be solved exactly. Solving this system with the Newton method for systems may result mo...

Biswas and Milovic proposed a generalized model for the NLSE that accounts for several imperfections in the fiber during long distance transmission of these pulses. This paper studies the exact solution of the BiswasMilovic equation with Kerr law nonlinearity by a new efficient method. The results reveal that the method is explicit, effective, and easy to use.