New Compacton Solutions and Solitary Pattern Solutions for Modified Nonlinearly Dispersive mK(m,n,a,b) Equation

In this paper exact solutions of a new modified nonlinearly dispersive equation （simply called inK（m, n, a, b） Ua Ub equation）, u^m-1 ut ＋ α（ u^n）x ＋β（u^a（u^b）xx）x = 0, is investigated by using some direct algorithms. As a result, abundant new compacton solutions （solitons with the absence of infinite wings） and solitary pattern solutions （having infinite slopes or cusps） are obtained.

Inertia-Centric Stability Analysis of a Planar Uniform Dust Molecular Cloud with Weak Neutral-Charged Dust Frictional Coupling

This paper adopts an inertia-centric evolutionary model to study the excitation mechanism of new gravito-electrostatic eigenmode structures in a one-dimensional（1-D） planar self-gravitating dust molecular cloud（DMC） on the Jeans scale.A quasi-neutral multi-fluid consisting of warm electrons,warm ions,neutral gas and identical inertial cold dust grains with partial ionization is considered.The grain-charge is assumed not to vary at the fluctuation evolution time scale.The neutral gas particles form the background,which is weakly coupled with the collapsing grainy plasma mass.The gravitational decoupling of the background neutral particles is justifiable for a higher inertial mass of the grains with higher neutral population density so that the Jeans mode frequency becomes reasonably large.Its physical basis is the Jeans assumption of a self-gravitating uniform medium adopted for fiducially analytical simplification by neglecting the zero-order field.So,the equilibrium is justifiably treated initially as ＂homogeneous＂.The efficacious inertial role of the thermal species amidst weak collisions of the neutral-charged grains is taken into account.A standard multiscale technique over the gravito-electrostatic equilibrium yields a unique pair of Korteweg-de Vries（KdV） equations.It is integrated numerically by the fourth-order Runge-Kutta method with multi-parameter variation for exact shape analyses.Interestingly,the model is conducive for the propagation of new conservative solitary spectral patterns.Their basic physics,parametric features and unique characteristics are discussed.The results go qualitatively in good correspondence with the earlier observations made by others.Tentative applications relevant to space and astrophysical environments are concisely highlighted.

Dissipative Discrete System with Nearest-Neighbor Interaction for the Nonlinear Electrical Lattice

A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This equation presents arbitrarily nearest-neighbor nonlinearities. We analyze the properties of such model both in connection to their modulational stability, as well as in regard to the generation of intrinsic localized modes. We present a generalized discrete Lange-Newell criterion. Numerical simulations are performed and we show that discrete breathers are generated through modulational instability.