Paper's Title:

Analysis of a Dynamic Elasto-viscoplastic Frictionless Antiplan Contact Problem with Normal Compliance

Author(s):

A. Ourahmoun¹, B. Bouderah², T. Serrar³

^1,2Applied Mathematics Laboratory,
M'sila University, 28000,
Algeria.
E-mail: ourahmounabbes@yahoo.fr

³Applied Mathematics Laboratory,
Setif 1 University, 19000,
Algeria.

Abstract:

We consider a mathematical model which describes the dynamic evolution of a thermo elasto viscoplastic contact problem between a body and a rigid foundation. The mechanical and thermal properties of the obstacle coating material near its surface. A variational formulation of this dynamic contact phenomenon is derived in the context of general models of thermo elasto viscoplastic materials. The displacements and temperatures of the bodies in contact are governed by the coupled system consisting of a variational inequality and a parabolic differential equation. The proof is based on a classical existence and uniqueness result on parabolic inequalities,differential equations and fixed point arguments.

Paper's Title:

The Projective Riccati Equations Method for Solving Nonlinear Schrodinger Equation in Bi-Isotropic Fiber

Author(s):

A. Ourahmoun, Z. Mezache

 Optics and Precision Mechanics Institute of Setif,
Algeria.
E-mail: abbes.ourahmoun@univ-setif.dz
zinemezaache@yahoo.fr
 

Abstract:

Bi-isotropic materials, characterized by their chiral and non-reciprocal nature, present unique challenges and opportunities in scientific research, driving the development of cutting-edge applications. In this paper, we explore the influence of chirality using a newly developed framework that emphasizes the nonlinear effects arising from the magnetization vector under a strong electric field. Our research introduces a novel formulation of constitutive relations and delves into the analysis of solutions for the nonlinear Schr\"{o}dinger equation, which governs pulse propagation in nonlinear bi-isotropic media. By employing the Projective Riccati Equation Method with variable dispersion and nonlinearity, we systematically derive families of solutions to the nonlinear Schr\"{o}dinger equation in chiral and non-reciprocal optical fibers. This approach provides valuable insights into the propagation of light in two polarization modes right circularly polarized (RCP) and left circularly polarized (LCP) each associated with distinct wave vectors in nonlinear bi-isotropic environments. The study presents several new exact solutions of optical solitons within these media.

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