A memory type boundary stabilization of a mildly damped wave equation

We consider the wave equation with a mild internal dissipation. It is proved that any small dissipation inside the domain is sufficient to uniformly stabilize the solution of this equation by means of a nonlinear feedback of memory type acting on a part of the boundary. This is established without any restriction on the space dimension and without geometrical conditions on the domain or its boundary

Soliton molecules in Fermi-Pasta-Ulam-Tsingou lattice: Gardner equation approach

We revisit the Fermi-Pasta-Ulam-Tsingou lattice (FPUT) with quadratic and cubic nonlinear interactions in the continuous limit by deducing the Gardner equation. Through the Hirota bilinear method, multi-soliton solutions are obtained for the Gardner equation. Based on these solutions, we show the excitation of an interesting class of table-top soliton molecules in the FPUT lattice through the velocity resonance mechanism. Depending on the condition on the free parameters, we classify them as dissociated and synthetic type molecules. The main feature of the table-top soliton molecules is that they do not exhibit oscillations in the coalescence region. This property ensures that they are distinct from the soliton molecules, having retrieval force, of the nonlinear Schr\"odinger family of systems. Further, to study the stability of the soliton molecule we allow it to interact with a single (or multi) soliton(s). The asymptotic analysis shows that their structures remain constant, though the bond length varies, throughout the collision process. In addition, we consider the FPUT lattice with quadratic nonlinear interaction and FPUT lattice with cubic nonlinearity as sub-cases and point out the nature of the soliton molecules for these cases also systematically. We achieve this based on the interconnections between the solutions of the Gardner, modified K-dV and K-dV equations. Finally, we simulate the FPUT chain corresponding to the Gardner equation numerically and verify the existence of all the soliton structures associated with it. We believe that the present study can be extended to other integrable and non-integrable systems with applications in fluid dynamics, Bose-Einstein condensates, nonlinear optics, and plasma physics.Comment: Submitted For Publication (2023

Coupled Nonlinear Schr\"odinger System: Role of Four-Wave Mixing Effect on Nondegenerate Vector Solitons

In this paper, we investigate the role of four-wave mixing effect on the structure of nondegenerate vector solitons and their collision dynamics. For this purpose, we consider the generalized coupled nonlinear Schr\"odinger (GCNLS) system which describes the evolution and nonlinear interaction of the two optical modes. The fundamental as well as higher-order nondegenerate vector soliton solutions are derived through the Hirota bilinear method and their forms are rewritten in a compact way using Gram determinants. Very interestingly, we find that the presence of four-wave mixing effect induces a breathing vector soliton state in both the optical modes. Such breather formation is not possible in the fundamental vector bright solitons of the Manakov system. Then, for both strong and weak four-wave mixing effects, we show that the nondegenerate solitons in the GCNLS system undergo, in general, novel shape changing collisions, in addition to shape preserving collision under suitable choice of wave numbers. Further, we analyze the degenerate soliton collision induced novel shape changing property of nondegenerate vector soliton by deriving the partially nondegenerate two-soliton solution. For completeness, the various collision scenarios related to the pure degenerate bright solitons are indicated. We believe that the results reported in this paper will be useful in nonlinear optics for manipulating light by light through collision.Comment: 23 pages, 15 figures, Submitted for publicatio

On Nonlinear Nonlocal Systems of Reaction Diffusion Equations

The reaction diffusion system with anomalous diffusion and a balance law ut+-Δα/2u=-fu,v,   vt+-∆β/2v=fu,v, 0<α, β<2, is con sidered. The existence of global solutions is proved in two situations: (i) a polynomial growth condition is imposed on the reaction term f when 0<α≤β≤2; (ii) no growth condition is imposed on the reaction term f when 0<β≤α≤2

Characterization of Streptomyces strain SLO-105 isolated from Lake Oubeira sediments in North-East of Algeria

A microbial strain, SLO-105, isolated from Lake Oubeira sediment was screened for its antimicrobial activity against pathogenic bacteria and fungi. The strain showed broad-spectrum antibacterial activity against Gram-positive bacteria Staphylococcus aureus MRSA, Bacillus subtilus, Micrococcus leutus,Streptococcus fecalis and fungi Aspergillus niger and Rodotorulla mucilaginosa. However, no activity of the strain was observed against Gram negative bacteria Escherichia coli and Pseudomonas aeruginosa as well as on fungi Candida albicans. Analysis of 16S rDNA sequence and themorphological and physiological characteristics of the strain suggested that the isolate belonged to Streptomyces genus

Exponential stability of the wave equation with memory and time delay

We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough