13 research outputs found
Time-Fractional KdV Equation for the plasma in auroral zone using Variational Methods
The reductive perturbation method has been employed to derive the Korteweg-de
Vries (KdV) equation for small but finite amplitude electrostatic waves. The
Lagrangian of the time fractional KdV equation is used in similar form to the
Lagrangian of the regular KdV equation. The variation of the functional of this
Lagrangian leads to the Euler-Lagrange equation that leads to the time
fractional KdV equation. The Riemann-Liouvulle definition of the fractional
derivative is used to describe the time fractional operator in the fractional
KdV equation. The variational-iteration method given by He is used to solve the
derived time fractional KdV equation. The calculations of the solution with
initial condition A0*sech(cx)^2 are carried out. Numerical studies have been
made using plasma parameters close to those values corresponding to the dayside
auroral zone. The effects of the time fractional parameter on the electrostatic
solitary structures are presented.Comment: 1 tex file + 5 eps figure
Formulation and Solution of Space-Time Fractional KdV-Burgers Equation
The space-time fractional KdV-Burgers equation has been derived using the semi-inverse method and Agrawal’s variational method. The modified Riemann-Liouville definition is used for the fractional differential operators. The derived fractional equation is solved using the fractional sub-equation method
Application of the Exp-Function Method to the Riccati Equation and New Exact Solutions with Three Arbitrary Functions of Quantum Zakharov Equations
The Exp-function method with the aid of the symbolic computational system is used for constructing generalized solitary solutions of the generalized Riccati equation. Based on the Riccati equation and its generalized solitary solutions, new exact solutions with three arbitrary functions of quantum Zakharov equations are obtained. It is shown that the Exp-function method provides a straightforward and important mathematical tool for nonlinear evolution equations in mathematical physics
Plasma Parameters Effects on Dust Acoustic Solitary Waves in Dusty Plasmas of Four Components
The presence and propagation of dust-acoustic solitary waves in dusty plasma contains four components such as negative and positive dust species beside ions and electrons are studied. Both the ions and electrons distributions are represented applying nonextensive formula. Employing the reductive perturbation method, an evolution equation is derived to describe the small-amplitude dust-acoustic solitons in the considered plasma system. The used reductive perturbation stretches lead to the nonlinear KdV and modified KdV equations with nonlinear and dispersion coefficients that depend on the parameters of the plasma. This study represents that the presence of compressive or/and rarefactive solitary waves depends mainly on the value of the first-order nonlinear coefficient. The structure of envelope wave is undefined for first-order nonlinear coefficient tends to vanish. The coexistence of the two types of solitary waves appears by increasing the strength of nonlinearity to the second order using the modified KdV equation