Nonlinear long wave propagation in a medium with periodic parameters is considered in the framework of a variable-coefficient Korteweg-de Vries equation. The characteristic period of the variable medium is varied from slow to rapid, and its amplitude is also varied. For the case of a piecewise constant coefficient with a large scale for each constant piece, explicit results for the damping of a...

The local stability of a nonlinear dynamical system at an equilibrium point with a pair of purely imaginary eigenvalues can be assessed through the computation of a cubic Hopf normal form coefficient, assuming the remaining eigenvalues have negative real parts. In this paper, a modal decomposition of the Hopf coefficient is proved. The decomposition provides a new methodology for analyzing the ...

We investigate the Nonlinear Schrödinger Equation with a timedependent nonlinear coefficient. By means of Painlevé analysis we establish the integrability of a particular case, when the nonlinear coefficient decays with t. The corresponding soliton solution is shown to be of the self-similar kind. We discuss implications of the result to the dynamics of attractive Bose-Einstein condensates unde...

in this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy fredholmintegro-differential equation of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an it...

In this study, the nonlinear optical properties and optical limiting performance of the silver nanoparticles (AgNPs) in distilled water are investigated. The nonlinear absorption coefficient of the colloid is measured by the Z-scan technique. The optical limiting behavior of the AgNP suspension is investigated under exposure to nanosecond laser pulses at 532 nm. The results show that nonlinear ...

in this paper, we use the parametric form of fuzzy numbers, and aniterative approach for obtaining approximate solution for a classof fuzzy nonlinear fredholm integral equations of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the fuzzy nonlinear integral equations by an iterativeapproach.