In studies of perturbation dynamics in physical systems certain specification of the governing perturbation dynamical system is generally lacking, either because the perturbation system is imperfectly known or because its specification is intrinsically uncertain, while a statistical characterization of the perturbation dynamical system is often available. In this report exact and asymptotically...

  Propagation of dust ion acoustic waves in plasmas composed of nonthermal distributed electrons and stationary dust particles is investigated. Nonlinear Schrdinger equation is derived to describe small amplitude waves, using the reduction perturbation technique. Modulation instability of dust ion acoustic waves is analysed for this system. Parametric investigation indicates that growth rate of...

Asymptotically exact and nonlocal third order nonlinear evolution equations are derivedfor two counterpropagating surface capillary gravity wave packets in deep water in thepresence of wind flowing over water.From these evolution equations stability analysis ismade for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. Instability condition is obtained and g...

The shear instability mechanism for generation of surface water waves (Miles 1957) is re-examined in light of the nonnormality of the underlying linear operator. The associated eigenproblem and adjoint eigenproblem are solved numerically and a clarification to previous perturbation solutions of the eigenproblem discussed. The optimal excitation problem is solved in the asymptotic limit t → ∞ an...

Abstract

A stochastic Gompertz model is proposed to study cancer growth with therapy. The reveals that the therapy and environmental fluctuation can control tumor size, but its extinction impossible. Optimal treatment suggested, probability density function elucidated clearly by Fokker-Planck equation.