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Higher Order Solitary Wave Solutions of the Standard KdV Equations

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Open Journal of Applied Sciences 2021年第1期11卷 103-125页

作者： Clovis Taki Djeumen Tchaho Hugues Martial Omanda Gaston N’tchayi Mbourou Jean Roger Bogning timoléon crépin kofané African Centre for Advanced Studies Yaoundé Cameroon Lycée Technique Fulbert Bongotha Moanda Gabon Laboratoire Pluridisciplinaire des Sciences Ecole Normale Supérieure Libreville Gabon Laboratoire de Mécanique des Matériaux Ecole Polytechnique Université des Sciences et Techniques de Masuku Franceville Gabon Department of Physics Higher Teacher Training College University of Bamenda Bamenda Cameroon Department of Physics Faculty of Science University of Yaoundé I Yaoundé Cameroon Centre d'Excellence Africain en Technologie de l'Information et de la Télécommunication University of Yaoundé I Yaoundé Cameroon

Considered under their standard form, the fifth-order KdV equations are a sort of reading table on which new prototypes of higher order solitary waves residing there, have been uncovered and revealed to broad daylight. The mathematical tool that made it possible to explore and analyze this equation is the Bogning-Djeumen Tchaho-kofané method extended to the new implicit Bogning' functions. The analytical form of the solutions chosen in this manuscript is particular in the sense that it contains within its bosom, a package of solitary waves made up of three solitons, especially, the bright type soliton, the hybrid soliton and the dark type soliton which we estimate capable in their interactions of generating new hybrid or multi-form solitons. Existence conditions of the obtained solitons have been determined. It emerges that, these existence conditions of the chosen ansatz could open the way to other new varieties of fifth-order KdV equations including to which it will be one of the solutions. Some of the obtained solitons are exact solutions. Intense numerical simulations highlighted numerical stability and confirmed the hybrid character of the obtained solutions. These results will help to model new nonlinear wave phenomena, in plasma media and in fluid dynamics, especially, on the shallow water surface.

关键词： Standard KdV Equations Bogning-Djeumen Tchaho-kofané Method Higher Order Solitary Wave Multi-Form Solitons New Implicit Bogning’ Functions

Hybrid Dispersive Optical Solitons in Nonlinear Cubic-Quintic-Septic Schrödinger Equation

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Optics and Photonics Journal 2021年第2期11卷 23-49页

作者： Clovis Taki Djeumen Tchaho Hugues Martial Omanda Gaston N’tchayi Mbourou Jean Roger Bogning timoléon crépin kofané African Centre for Advanced Studies Yaoundé Cameroon Lycée Technique Fulbert Bongotha Moanda Gabon Laboratoire Pluridisciplinaire des Sciences Ecole Normale Sup&#233 rieure Libreville Gabon Laboratoire de Mécanique des Matériaux Ecole Polytechnique Université des Sciences et Techniques de Masuku Franceville Gabon Department of Physics Higher Teacher Training College University of Bamenda Bamenda Cameroon Department of Physics Faculty of Science University of Yaoundé I Yaoundé Cameroon Centre d’Excellence Africain en Technologie de l’Information et de la Télécommunication University of Yaoundé I Yaoundé Cameroon

Certain hybrid prototypes of dispersive optical solitons that we are looking for can correspond to new or future behaviors, observable or not, developed or will be developed by optical media that present the cubic-quintic-septic law coupled, with strong dispersions. The equation considered for this purpose is that of non-linear Schrödinger. The solutions are obtained using the Bogning-Djeumen Tchaho-kofané method extended to the new implicit Bogning’ functions. Some of the obtained solutions show that their existence is due only to the Kerr law nonlinearity presence. Graphical representations plotted have confirmed the hybrid and multi-form character of the obtained dispersive optical solitons. We believe that a good understanding of the hybrid dispersive optical solitons highlighted in the context of this work allows to grasp the physical description of systems whose dynamics are governed by nonlinear Schrödinger equation as studied in this work, allowing thereby a relevant improvement of complex problems encountered in particular in nonliear optaics and in optical fibers.

关键词： Nonlinear Schrödinger Equation Bogning-Djeumen Tchaho-kofané Method Hybrid Dispersive Optical Solitons Cubic-Quintic-Septic Law Strong Dispersions Nonlinear Optics

Transcription's bubble under the influence of long-range interactions and helicoidal coupling

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Chinese Physics B 2013年第12期22卷 589-602页

作者： Mirabeau Saha timolon C.kofan Laboratory of Mechanics Department of Physics Faculty of Science University of Yaounde' P. O. Box 812 Yaounde' Cameroon The Abdus Salam International Center for Theoretical Physics P. O. Box 586 Strada Costiera 11 I-34014 Trieste Italy

The influence of power-low long-range interactions （LRI） and helicoidal coupling （HC） on the properties of localized solitons in a DNA molecule when a ribonucleic acid polymerase （RNAP） binds to it at the physiological temperature is analytically and numerically investigated in this paper. We have made an analogy with the Heisenberg model Hamiltonian of an anisotropic spin ladder with ferromagnetic legs and anti-ferromagnetic rung coupling. When we limit ourselves to the second-order terms in the Taylor expansion, the DNA dynamics is found to be governed by a completely integrable nonlinear Schr？dinger （NLS） equation. In this case, results show that increasing the value of HC force or LRI parameter enhances the bubble height and reduces the number of base pairs which form the bubble. For the fourth-order terms in a Taylor expansion, results are closely resembling those of second-order terms, and are confirmed by numerical investigation. These results match with some experimental data and thus provide a better representation of the base pairs opening in DNA which is essential for the transcription process.

关键词： DNA helicoidal coupling RNA-polymerase spin model Riemann zeta function power-law long-range interaction breather-like soliton

Matter-wave solutions of Bose-Einstein condensates with three-body interaction in linear magnetic and time-dependent laser fields

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Chinese Physics B 2012年第7期21卷 187-192页

作者： Etienne Wamba timolon C. kofan Alidou Mohamadou Laboratory of Mechanics Department of Physics Faculty of Science University of Yaound I Condensed Matter Laboratory Department of Physics Faculty of Science University of Douala The Abdus Salam International Centre for Theoretical Physics

We construct, through a further extension of the tanh-function method, the matter-wave solutions of Bose-Einstein condensates （BECs） with a three-body interaction. The BECs are trapped in a potential comprising the linear magnetic and the time-dependent laser fields. The exact solutions obtained include soliton solutions, such as kink and antikink as well as bright, dark, multisolitonic modulated waves. We realize that the motion and the shape of the solitary wave can be manipulated by controlling the strengths of the fields.

关键词： extended tanh-function method Gross Pitaevskii equation cubic quintic nonlinearity,soliton solutions

Discrete energy transport in collagen molecules

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Chinese Physics B 2014年第9期23卷 544-548页

作者： Alain Mvogo Germain H.Ben-Bolie timoléon C.kofané Laboratory of Biophysics Department of PhysicsFaculty of ScienceUniversity of Yaounde I Laboratory of Nuclear Physics Department of PhysicsFaculty of ScienceUniversity of Yaounde I Centre d'Excellence Africain en Technologies de l'Information et de la Communication University of Yaounde I Laboratory of Mechanics Department of PhysicsFaculty of ScienceUniversity of Yaounde I

The modulational instability in the three coupled α-polypeptide chains of a collagen molecule is investigated. Choosing symmetric and asymmetric solutions, and applying the so-called rotating-wave approximation, we describe the dynamics of the system by the discrete nonlinear Schrodinger （DNLS） equation. The linear stability analysis of the continuous wave solution is performed. The numerical simulations show the generation of trains of solitonic structures in the lattice with increasing amplitude as time progresses. The effect of damping and noise forces of the physiological temperature （T = 300 K） introduces an erratic behavior to the formed patterns, reinforcing the idea that the energy used in metabolic processes is confined to specific regions for efficiency.

关键词： modulational instability collagen molecules damping noise force

Dry Friction with Various Frictions Laws: From Wave Modulated Orbit to Stick-Slip Modulated

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Modern Mechanical Engineering 2015年第2期5卷 28-40页

作者： Paul Ndy Von Kluge Djuidjé Kenmoé Germaine kofané timoléon crépin Department of Physics Mechanics Laboratory Faculty of Sciences University of Yaoundé 1 Yaoundé Cameroon

Choices of excitation signals are important in engineering sciences and in physical simulations;a sufficient excitation can be critical in modelling a complicated nonlinear dynamic system. The discontinuous dynamic of a non-linear, friction-induced with two idealized periodical forced oscillators is studied. The dry friction in the system follows the classical Coulomb law, and various friction characteristics of dry friction laws in engineering sciences. To capture the presence of the two driving forces, the system must be studied as a function of their frequency-modulated and its equivalent amplitude modulated waveforms. Our numerical investigation shows a rich dynamical behaviour including periodic, quasi-periodic motions, thus a variable dynamics phenomenon among others;such as modulated waves, modulated stick-slip, periodic oscillation, and periodic stick-slip. It seems that such excitation forces can be used to conveniently identify the existence of nonlinearity, dry friction effects, and strength degradation in the system. The results achieved via the Coulomb’s law are compared with those obtained via two others particular friction laws: the complete model with Stribeck effect and Coulomb viscosity.

关键词： Dry Friction Stick-Slip Wave Modulated Stick-Slip Modulated

crustal Structure and Tectonic Setting over the Panafrican Domain in Loum-Minta Area (Centre-East Cameroon) from Aeromagnetic Analysis

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Journal of Geoscience and Environment Protection 2019年第4期7卷 61-81页

作者： Jean Aimé Mono Marcelin Bikoro Bi-Alou Arsene Meying Theophile Ndougsa-Mbarga Stéphane Patrick Assembe crépin timoléon kofané Postgraduate School of Sciences Technologies & Geosciences University of Yaoundé I Yaoundé Cameroon Basical Sciences Teaching Department of Advanced Technical Teacher Training School University of Douala Douala Cameroon Department of Earth Sciences Faculty of Science University of Maroua Maroua Cameroon School of Geology and Mining Engineering University of Ngaoundere Ngaoundere Cameroon Department of Physics Advanced Teacher’s Training College University of Yaoundé I Yaoundé Cameroon Faculty of Science University of Bamenda Bambili Cameroon

The present work aims to determine the geological structure, to highlight and to determine the characteristics of the fault system responsible for the current structure of the study area through the interpretation of available aeromagnetic data. Total magnetic intensity anomaly (TMI) was critically interpreted using several analysis techniques including Reduction to Equator (RTE), First Vertical Derivative, upward continuation, spectral analysis and 2D3/4 modelling. All results obtained from the interpretation process were combined together to draw an interpretative geological map of the area and allow the general view of the surface and sub-surface structures. The interpretative geological map reveals that the geological formations of the studied area appear to be intensely fractured by an E-W, ENE-WSW and NE-SW main orientation fault system. The lineaments identified in the area study could be linked to the Pan-African orogeny and seem to correspond to deep-seated basement structures, which are referred to the tectonic boundary between Congo craton and the Pan-African orogeny belt. According to spectral analysis results, the depths of the sources of superficial and deep magnetic anomalies are 2500 m and 12,000 m respectively. The 2D3/4 modelling of one magnetic profile plotted on the reduced residual map at the equator was performed to approximate the geometry and depth of the sources of magnetic anomalies, the model suggests the intrusion of a large body of high susceptibility during the continental collision. The results of this study can be used to better understand deep-seated basement structures and to support decisions with regard to the development of industrial areas, as well as of hydrogeological and/or mining investigations to be undertaken in the study area.

关键词： Aeromagnetic Upward Continuation Spectral Analysis Modelling 2D3/4

Modulated Wave Packets in DNA and Impact of Viscosity

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Chinese Physics Letters 2009年第6期26卷 294-297页

作者： Conrad Bertrand Tabi Alidou Mohamadou timoleon crepin kofané Laboratory of Mechanics Department of Physics Faculty of Science University of Yaounde I PO Box 812 Yaounde Cameroon Condensed Matter Laboratory Department of Physics Faculty of Science University of Douala PO Box 24157 Douala Cameroon

我们在生理的温度学习一个 DNA 分子的系统的非线性的动力学在一粘滞由使用 Peyrard 主教的媒介当模特儿。上述系统的非线性的动力学被显示被分离复杂 Ginzburg 四轮马车方程管理。在非粘滞的限制，方程归结为非线性的 Schrödinger 方程... 详细信息

我们在生理的温度学习一个 DNA 分子的系统的非线性的动力学在一粘滞由使用 Peyrard 主教的媒介当模特儿。上述系统的非线性的动力学被显示被分离复杂 Ginzburg 四轮马车方程管理。在非粘滞的限制，方程归结为非线性的 Schrödinger 方程。Modulational 不稳定性标准为两个被导出案例。根据这些标准，数字模拟被做，它证实分析预言。用作起始的条件的平面波浪答案做基础对和原因精力本地化的局部性的摆动。结果也证明在包围的溶剂的粘性外面抑制波浪模式的振幅。

关键词：调制不稳定性非线性Schroedinger方程 DNA 粘度非线性动力学系统波包 Landau 生理温度