In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plan...

are smooth, given that k is smooth and nonnegative. When u is radial, (1) reduces to a nonlinear ODE on [0, 1) that is singular at the endpoint 0. It is thus easy to prove that u is always smooth away from the origin, even where k vanishes, but smoothness at the origin is more complicated, and determined by the order of vanishing of k there. In fact, Monn [9] proves that if k = k (x) is indepen...

The problem of the prescribed curvature measure is one important problems in differential geometry and nonlinear partial equations. In this paper, we consider hyperbolic space. We obtain existence star-shaped k-convex bodies with (n-k)-th measures (k<n) by establishing crucial C^2 regularity estimates for solutions to corresponding fully PDE

parameter estimation is an important task in the modeling, classification, and detection of radar clutters. radar clutters have stochastic characteristics. therefore, statistical distributions are usually used to describe the features of clutters better. k distribution is one of the most common models utilized to the simulation of clutters. this distribution, which consists of scale and shape p...

We establish the future stability of nonlinear perturbations a class homogeneous solutions to relativistic Euler equations with linear equation state $p=K\rho$ on exponentially expanding FLRW spacetimes for parameter values $1/3 < K 1/2$.

Propagation criterion of degree l and order k (PC(l) of order k) and resiliency of vectorial Boolean functions are important for cryptographic purpose (see [1, 2, 3, 6, 7,8,10,11,16]. Kurosawa , Stoh [8] and Carlet [1] gave a construction of Boolean functions satisfying PC(l) of order k from binary linear or nonlinear codes. In this paper, algebraic-geometric codes over GF (2) are used to modif...

In this paper, we propose a novel Spatial Clustering with Obstacles Constraints (SCOC) based on Dynamic Piecewise Linear Chaotic Map and Dynamic Nonlinear Particle Swarm Optimization (PNPSO) and K-Medoids, which is called PNPKSCOC. The contrastive experiments show that PNPKSCOC is effective and has better practicalities, and it performs better than PSO K-Medoids SCOC in terms of quantization er...

We consider the higher-order nonlinear difference equation xn 1 α xn / A Bxn xn−k , n 0, 1, . . ., where parameters are positive real numbers and initial conditions x−k, . . . , x0 are nonnegative real numbers, k ≥ 2. We investigate the periodic character, the invariant intervals, and the global asymptotic stability of all positive solutions of the abovementioned equation. We show that the uniq...

Given a power grid modeled by a network together with equations describing power flows, power generation and consumption, the so-called N − k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. The case where k is small is of practical interest. We present theoretical and numerical results involving a mixed-integer linear model and a continuou...

Our aim in this paper is to investigate the global attractivity of all positive solutions of the higher order nonlinear difference equation xn+1 = a+ bxn A−∑k i=0 bixn−i , n = 0, 1, . . . , where A, b, bk ∈ (0,∞), a, b0, . . . , bk−1 ∈ [0,∞), k ∈ {1, 2, . . .} and the initial conditions x−k, . . . , x0 are arbitrary. We show that one positive equilibrium of the equation is a global attractor wi...