Solitary and blow-up electrostatic excitations in rotating magnetized electron-positron-ion plasmas

The nonlinear dynamics of a rotating magnetoplasma consisting of electrons, positrons and stationary positive ions is considered. The basic set of hydrodynamic and Poisson equations are reduced to a Zakharov-Kuznetsov (ZK) equation for the electric potential. The ZK equation is solved by applying an improved modified extended tanh-function method (2008 Phys. Lett. A 372 5691) and its characteristics are investigated. A set of new solutions are derived, including localized solitary waves, periodic nonlinear waveforms and divergent (explosive) pulses. The characteristics of these nonlinear excitations are investigated in detail

Exact travelling solutions of two coupled (2 + 1)-Dimensional Equations

Extended tanh method is examined to solve the coupled Burgers system and the modified KdV–Boiti–Leon–Manna–Pempinelli (mKdV–BLMP) system. The exact travelling wave solutions are obtained. The obtained solutions include rational, periodical, singular and solitary wave solutions

Traveling wave solutions for shallow water equations

An extended homogeneous balance method is suggested in this paper. Based on computerized symbolic computation and the homogeneous balance method, new exact traveling wave solutions of nonlinear partial differential equations (PDEs) are presented. The shallow-water equations represent a simple yet realistic set of equations typically found in atmospheric or ocean modeling applications, we consider the exact solutions of the nonlinear generalized shallow water equation and the fourth order Boussinesq equation. Applying this method, with the aid of Mathematica, many new exact traveling wave solutions are successfully obtained

Analytical Wave Solutions for Foam and KdV-Burgers Equations Using Extended Homogeneous Balance Method

In this paper, extended homogeneous balance method is presented with the aid of computer algebraic system Mathematica for deriving new exact traveling wave solutions for the foam drainage equation and the Kowerteg-de Vries–Burgers equation which have many applications in industrial applications and plasma physics. The method is effective to construct a series of analytical solutions including many types like periodical, rational, singular, shock, and soliton wave solutions for a wide class of nonlinear evolution equations in mathematical physics and engineering sciences

Ion-acoustic solitary waves in a dense pair-ion plasma containing degenerate electrons and positrons

Fully nonlinear propagation of ion-acoustic solitary waves in a collisionless dense/quantum electron-positron-ion plasma is investigated. The electrons and positrons are assumed to follow the Thomas-Fermi density distribution and the ions are described by the hydrodynamic equations. An energy balance-like equation involving a Sagdeev-type pseudo-potential is derived. Finite amplitude solutions are obtained numerically and their characteristics are discussed. The small-but finite-amplitude limit is also considered and an exact analytical solution is obtained. The present studies might be helpful to understand the excitation of nonlinear ion-acoustic solitary waves in a degenerate plasma such as in superdense white dwarfs

Localized electrostatic excitations in a thomas-fermi plasma containing degenerate electrons

By using the Thomas-Fermi electron density distribution for quantum degenerate electrons, the hydrodynamic equations for ions, and the Poisson equation, planar and nonplanar ion-acoustic solitary waves in an unmagnetized collisionless plasma are investigated. The reductive perturbation method is used to derive cylindrical and spherical Korteweg-de Vries equations. Numerical solutions of the latter are presented. The present results can be useful in understanding the features of small but finite amplitude localized ion-acoustic solitary pulses in a degenerate plasm