Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

The connections among the various nonlinearity criteria is currently an important topic in the area of designing and analyzing cryptographic functions. In this paper we show a quantitative relationship between propagation characteristics and nonlinearity, two critical indicators of the cryptographic strength of a Boolean function. We also present a tight lower bound on the nonlinearity of a cry...

We predict a strong effective Kerr nonlinearity in hollow-core photonic crystal fibers filled with a Raman active gas which exceeds the intrinsic Kerr nonlinearity by 2 orders of magnitude. Two-color bright-bright and dark-bright solitons supported by this nonlinearity are found and the feasibility of their experimental observation is demonstrated.

The connections among the various nonlinearity criteria is currently an important topic in the area of designing and analyzing cryptographic functions In this paper we show a quantitative relationship between propagation characteristics and nonlinearity two critical indicators of the cryptographic strength of a Boolean function We also present a tight lower bound on the nonlinearity of a crypto...

Nonlinearity, 0-1 balancedness and strict avalanche criterion (SAC) are important criteria for cryptographic functions. Bent functions have maximum nonlinearity and satisfy SAC however they are not 01 balanced and hence cannot be directly used in many cryptosystems where 0-1 balancedness is needed. In this paper we construct (i) 0-1 balanced boolean functions on V2k+1 (k ≥ 1) having nonlinearit...

We present a chaotic frequency-modulated microwave source that is governed by a simple, first-order nonlinear delay differential equation. When a sinusoidal nonlinearity is incorporated, the dynamical behaviors range from fixed-point to periodic to chaotic, depending on the feedback strength. When the sinusoidal nonlinearity is replaced by a binary nonlinearity, the system exhibits a complex pe...

This paper carries out the integration of the resonant nonlinear Schrödinger’s equation in presence of perturbation terms that are considered with full nonlinearity. The three types of nonlinear media are studied. They are the cubic nonlinearity, power law and log law nonlinearity. The semi-inverse variational principle is applied to extract the analytical soliton solution.

We study the inverse scattering problem for the three dimensional nonlinear Schrödinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of the scattering states. Our result is applicable to reconstructing the nonlinearity of the semi-relativistic Hartree equation.