Gambo Betchewe

Soliton wave solutions for the nonlinear transmission line using the Kudryashov method and the (G′/G)-expansion method

Abstract This work focuses on finding soliton solutions in a nonlinear transmission line. By applying the Kirchhoff’s laws and the continuum approximation to a nonlinear electrical line, we arrive at the equation of wave propagation. Solving this equation through the Kudryashov method and the ( G ′ / G ) -expansion method provides kink, antikink and breather soliton solutions. In view of the obtained results, the Kudryashov method and the ( G ′ / G ) -expansion method are potential candidates which can be extended to other nonlinear transmission lines.

Dynamical survey of a generalized-Zakharov equation and its exact travelling wave solutions

We investigate the dynamical behavior of a generalized-Zakharov equation for the complex envelope of the high-frequency wave and the real low-frequency field by analyzing its phase portraits. Following a dynamical system approach, in different parameter regions, we depict phase portraits of a travelling wave system. Through discussing the bifurcation of phase portraits, we unwrap explicit miscellaneous travelling waves including localized and periodic ones. 2010 Elsevier Inc. All rights reserved.

Exact solutions of a semiconductor nonlinear reaction diffusion equation through factorization method

Abstract In this paper, we investigate exact solutions of the semiconductor reaction diffusion equation which is physically related to the one level impact ionization phenomenon. As a result, following the factorization method, we obtain the electrons density which behaves as a kink solution. We also find the electric field through Taylor series.

Travelling Wave Solutions to Stretched Beam's Equation: Phase Portraits Survey

In this paper, following the phase portraits analysis, we investigate the integrability of a system which physically describes the transverse oscillation of an elastic beam under end-thrust. As a result, we find that this system actually comprises two families of travelling waves: the sub- and super-sonic periodic waves of positive- and negative-definite velocities, respectively, and the localized sub-sonic loop-shaped waves of positive-definite velocity. Expressing the energy-like of this system while depicting its phase portrait dynamics, we show that these multivalued localized travelling waves appear as the boundary solutions to which the periodic travelling waves tend asymptotically.

Miscellaneous Rotating Solitary Waves to a Coupled Dispersionless System

We investigate the soliton structure of a coupled dispersionless system describing a current-conducting string with infinite length within a magnetic field. Thus, following Hirotas method, we unwrap three typical localized waves with nonzero angular momentum depending strongly upon their angular velocities. Illustrating the soliton behavior of these waves, we focus our interests on breather-like waves and depict the elastic scattering amongst such waves.