Kuetche Kamgang Victor

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.

On High-Frequency Soliton Solutions to a (2+1)-Dimensional Nonlinear Partial Differential Evolution Equation

A (2+1)-dimensional nonlinear partial differential evolution (NLPDE) equation is presented as a model equation for relaxing high-rate processes in active barothropic media. With the aid of symbolic computation and Hirotas method, some typical solitary wave solutions to this (2+1)-dimensional NLPDE equation are unearthed. As a result, depending on the dissipative parameter, single and multivalued solutions are depicted.

The structures and interactions of solitary waves in a (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation

The complete integrability of a (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion (CNLERD) equation using the technique of Painlev(P)-analysis is investigated. Using the formalism of Weiss et al (1983 J. Math. Phys. 24 522), the arbitrariness of the expansion coefficients are proved. Besides, following the Hirotas formalism (Hirota R 1980 Direct methods in soliton theory Soliton (Berlin: Springer)) combined to Weiss et als methodology (Weiss et al 1984 J. Math. Phys. 25 13), the consistency of the truncation is shown. Thus, without the use of Kruskals simplification, the Bcklund transformation (BT) of the equations is obtained via the truncation procedure. Taking into account the arbitrariness of the expansion coefficients in the foregoing truncation, a typical spectrum of localized coherent structures may be unearthed. The scattering behavior of such structures is also investigated.

Algebraic structure of a generalized coupled dispersionless system

We study a physical model of the O(3)-invariant coupled integrable dispersionless equations that describes the dynamic of a focused system within the background of a plane gravitational field. The investigation is carried out both numerically and analytically, and realized beneath some assumptions superseding the structure constant with the structure function implemented in Lie algebra and quasigroup theory, respectively. The energy density and topological structures such as loop soliton are examined.

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.

Prolongation Structure Analysis of a Coupled Dispersionless System

We address the problem of integrability of a coupled dispersionless system recently introduced by Zhaqilao, Zhao and Li [Chin. Phys. B 18 (2009) 1780] which physically describes the propagation of electromagnetic fields within an optical nonlinear medium, but also arrives in the physical description of a charged object dynamics in an external magnetic field. Following the prolongation structure analysis developed by Wahlquist and Estabrook, we derive a more general form of Lax pairs of the previous coupled dispersionless system and its concrete non-Abelian Lie algebra resorting to a hidden symmetry. Also, we construct the Backlund transformation of the system using the Riccati form of the linear eigenvalue problem.

Dynamical System Approach to a Coupled Dispersionless System: Localized and Periodic Traveling Waves

We investigate the dynamical behavior of a coupled dispersionless system describing a current-conducting string with infinite length within a magnetic field. Thus, following a dynamical system approach, we unwrap typical miscellaneous traveling waves including localized and periodic ones. Studying the relative stabilities of such structures through their energy densities, we find that under some boundary conditions, localized waves moving in positive directions are more stable than periodic waves which in contrast stand for the most stable traveling waves in another boundary condition situation.

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.

Initial-Value Problem of a Coupled Dispersionless System: Dynamical System Approach

We investigate the dynamical behaviour of a coupled dispersionless system (CDS) by solving its initial-value problem following a dynamical system approach. As a result, we unearth a typical miscellaneous travelling waves including the localized and periodic ones. We also investigate the energy density of such waves and find that under some boundary conditions, the localized waves moving towards positive direction are more stable than the periodic waves which on contrary stand for the most stable travelling waves in another situation of boundary conditions.

On the Conversion of High-Frequency Soliton Solutions to a (1+1)-Dimensional Nonlinear Partial Differential Evolution Equation

From the dynamical equation of barotropic relaxing media beneath pressure perturbations, and using the reductive perturbative analysis, we investigate the soliton structure of a (1+1)-dimensional nonlinear partial differential evolution (NLPDE) equation δy(δ + uδy + (u2/2) δy)u + αuy + u = 0, describing high-frequency regime of perturbations. Thus, by means of Hirotas bilinearization method, three typical solutions depending strongly upon a characteristic dissipation parameter are unearthed.