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Exact Solutions of Forced Schrödinger Equation and How to Choose the External Forces

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Journal of Applied Mathematics and Physics 2024年第10期12卷 3521-3537页

作者： Marcelle Nina Zambo Abou’ou jean roger bogning Department of Physics Faculty of Science University of Bamenda Bamenda Cameroon Department of Physics Higher Teacher Training College University of Bamenda Bamenda Cameroon African Optical Fiber Family Campost Kamkop Bafoussam Cameroon

Schrödinger equations are very common equations in physics and mathematics for nonlinear physics to model the dynamics of wave propagation in waveguides such as power lines, atomic chains, optical fibers, and even in quantum mechanics. But all these equations are most often studied without worrying about what would happen if this equation were maintained, that is to say, had a second member synonymous with an external force. It is true that on a physical level, such equations can be considered as describing the generation of waves on a waveguide using an external force. However, the in-depth analysis of this aspect is not at the center of our reflection in this article, but for us, it is a question of proposing exact solutions to this type of equation and above all proposing the general form of the external force so that the obtaining exact solutions is possible.

关键词： Schrödinger Equation Solitary Wave Exact Solutions External Forces iB-Functions

Selective Impact of Dispersion and Nonlinearity on Waves and Solitary Wave in a Strongly Nonlinear and Flattened Waveguide

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Open Journal of Applied Sciences 2024年第7期14卷 1730-1753页

作者： Christian Regis Ngouo Tchinda Marcelle Nina Zambo Abou’ou jean roger bogning Department of Physics Faculty of Science University of Yaound I Yaound Cameroon Centre dExcellence Africain en Technologie de lInformation et de la Tlcommunication The University of Yaound I Yaound Cameroon African Optical Fiber Family Bafoussam Cameroon Department of Physics Faculty of Science University of Bamenda Bamenda Cameroon Department of Physics Higher Teacher Training College University of Bamenda Bamenda Cameroon

The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions.

关键词： Flattened Waveguide Solitary Wave Characteristic Coefficient Probabilities Propagation Nonlinear Dispersive Partial Differential Equation

Sasa-Satsuma’s Dynamical Equation and Optical Solitary Wave Solutions

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Optics and Photonics Journal 2022年第5期12卷 128-145页

作者： Clovis Taki Djeumen Tchaho jean Pierre Ngantcha Hugues Martial Omanda Bruno Rodin Mbock Um Thierry Blanchard Ekogo jean roger bogning African Centre for Advanced Studies Yaoundé Cameroon Lycée Technique Fulbert Bongotha Moanda Gabon Laboratoire de Mécanique des Matériaux Ecole Polytechnique Université des Sciences et Techniques de Masuku Franceville Gabon Laboratoire Pluridisciplinaire des Sciences Ecole Normale Supérieure Libreville Gabon Département de Physique Université des Sciences et Techniques de Masuku Franceville Gabon Institut International de Recherches Biomédicales et de Biotechnologies Carl Kambangoye (IRBK) Université Internationale de Libreville (UIL) Libreville Gabon Department of Physics Higher Teacher Training College University of Bamenda Bamenda Cameroon

This work proposes the construction of a prototype of pulse-kink hybrid solitary waves with a strong Kink dosage of the Sasa-Satsuma equation which describes the dynamics of the wave propagating in an optical fiber where the stimulated Raman scattering effect is bethinking during modeling. The ultimate goal of this work is to propose a plateful of solutions likely to serve as signals during studies on computer or laboratory propagation studies. The resolution of such an equation is not always the easiest thing, and we used the bogning-Djeumen Tchaho-Kofané method extended to the implicit functions of bogning to obtain the results. The flexibility of the iB-functions made it possible to deduce the trigonometric solutions, from the obtained solitary wave solutions with a hyperbolic analytical sequence of the studied Sasa-Satsuma equation. A better appreciation of the nature of the solutions obtained is made through the profiles of some solutions obtained during the different analyses.

关键词： Sasa-Satsuma’s Dynamical Equation bogning-Djeumen Tchaho-Kofané Method Optical Soliton iB-Functions Stimulated Raman Scattering

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

Construction of New Surface Wave Solutions of the Modified KdV Equation

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Open Journal of Applied Sciences 2022年第2期12卷 196-215页

作者： Clovis Taki Djeumen Tchaho jean Pierre Ngantcha Thierry Blanchard Ekogo Bruno Rodin Mbock Um Hugues Martial Omanda Hugues Martial Omanda jean roger bogning African Centre for Advanced Studies Yaoundé Cameroon Lycée Technique Fulbert Bongotha Moanda Gabon Laboratoire de Mécanique des matériaux école Polytechnique Université des Sciences et Techniques de Masuku Franceville Gabon Département de Physique Université des Sciences et Techniques de Masuku Franceville Gabon Institut International de Recherches Biomédicales et de Biotechnologies Carl Kambangoye (IRBK) Université Internationale de Li-breville (UIL) Libreville Gabon Laboratoire Pluridisciplinaire des Sciences école Normale Supérieure Libreville Gabon Department of Physics Higher Teacher Training College University of Bamenda Bamenda Cameroon

The major concern of this work is to propose new prototypes of surface hybrid waves, in particular waves propagating without sprawl or deformation on the surface of a fluid. The model considered for this purpose is the modified KdV (Korteweg-de Vries) equation. A peculiarity of the obtained solutions is that they form packages constituted by combinations of waves belonging to the two main families of well-known bright and dark solitary waves. This putting together creates competitions between the different components of the considered packages which, following the values assigned to the parameters of the considered system and in relation to those of the wave parameters, generate hybrid or multi-form structures. The direct method of resolution which made possible the obtained results is that of bogning-Djeumen Tchaho-Kofane extended to the new implicit bogning functions. The existence conditions of some solutions are obtained. The numerical simulations carried out with a view to testing the observable and applicable characters of the obtained solutions revealed their stabilities over a relatively long time, and at the same time, confirmed the recommended theoretical forecasts. We are convinced that the solutions proposed as part of this work will make it possible to detect, understand and explain some physical phenomena linked to fluid molecular interactions, former or new, which constantly occur on the fluid surfaces, mainly at the shallow water surface.

关键词： Surface Hybrid Waves Modified Korteweg-De Vries Equation bogning-Djeumen Tchaho-Kofané Method Hybrid Prototypes Multi-Form Structures

Influence of Waveguide Properties on Wave Prototypes Likely to Accompany the Dynamics of Four-Wave Mixing in Optical Fibers

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Journal of Applied Mathematics and Physics 2024年第7期12卷 2601-2633页

作者： jean roger bogning Marcelle Nina Zambo Abou’ou Christian Regis Ngouo Tchinda Mathurin Fomekong Oriel Loh Ndichia Stallone Mezezem Songna François Béceau Pelap Department of Physics Higher Teacher Training College University of Bamenda Bamenda Cameroon African Optical Fiber Family Bafoussam Cameroon Department of Physics Faculty of Science University of Bamenda Bamenda Cameroon Department of Physics Faculty of Science University of Yaound I Yaound Cameroon Africain en Technologie de lInformation et de la Tlcommunication The University of Yaound I Yaound Cameroon Unit de Recherche de Mcanique et de Modlisation des Systmes Physiques (UR-2MSP) Facult des Sciences Universit de Dschang Dschang Cameroun

In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of the iB-function to first decouple the nonlinear partial differential equations that govern the propagation dynamics in this case, and subsequently solve them to propose some prototype solutions. These analytical solutions have been obtained;we check the impact of nonlinearity and dispersion. The interest of this work lies not only in the resolution of the partial differential equations that govern the dynamics of wave propagation in this case since these equations not at all easy to integrate analytically and their analytical solutions are very rare, in other words, we propose analytically the solutions of the nonlinear coupled partial differential equations which govern the dynamics of four-wave mixing in optical fibers. Beyond the physical interest of this work, there is also an appreciable mathematical interest.

关键词： Optical Fiber Four Waves Mixing Implicit bogning Function Coupled Nonlinear Partial Differential Equations Nonlinear Coefficient Dispersive Coefficient Waveguide Properties

Epidemiological, Clinical and Etiological Aspects of Non-Traumatic Comas in Children at the Pediatric Teaching Hospital in Bangui

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Open Journal of Pediatrics 2022年第3期12卷 489-506页

作者： Olivier Brice bogning Mejiozem Moyen Engoba Evodie Pierrette bogning Kakounguere jean Chrysostome Gody Centre Hospitalier Universitaire Pédiatrique de Bangui Bangui Central African Republic Université Marien Ngouabi Brazzaville Republic of the Congo Faculté des Sciences de la Santé de l’Université de Bangui Bangui Central African Republic

Background: Non-traumatic coma is the most common pediatric medical emergency. Its clinical diagnosis is easy. The difficulty lies in finding the etiology. Objective: To determine the prevalence and clinical profiles of non-traumatic Coma at the Centre Hospitalier Universitaire Pédiatrique de Bangui (CHUPB). Methodology: This was a descriptive and analytical cross-sectional study conducted between January 1 and June 31, 2021, at CHUPB. Children aged 1 month to 15 years, admitted to the emergency room with a Glasgow score less than or equal to 8 without any traumatism were included. The variables studied were sociodemographic, clinical and paraclinical. Data were entered and analyzed using SPSS 20.0 statistical software. The statistical test used was Pearson’s chi2, any p-value Results: Of 8551 children hospitalized during the study period, 370 were hospitalized for non-traumatic coma: 4.32%. They were divided into 57.5% (n = 213) boys and 42.44% (n = 157) girls, giving a sex ratio of 1.35. Their mean age was 35.95 ± 27.21 months. Children aged 1 to 24 months represented 54.59% (n = 202) of cases. The mean time to the consultation was 2.91 days ± 1.8. Fever 86.48% (n = 320) and convulsions 80% (n = 296) were the main reasons for consultation. Coma stages II - III and IV represented 52.44% (n = 194), 42.97% (n = 159) and 4.59% (n = 17) respectively. Neuromalaria (29.72%;n = 110), meningitis-meningoencephalitis-encephalitis (30%;n = 111), sepsis (19.72%;n = 73) and acidosis Coma (5.40%;n = 20) were the main etiologies. Conclusion: Non-traumatic coma is common at CHUPB. Infections were the main etiology, particularly cerebral malaria. The reduction of its frequency requires, among others, the strengthening of the national monitoring malaria program. The strengthening of the technical platform for a good etiological diagnosis constitutes the other axis of prevention.

关键词： Non-Traumatic Coma Child Epidemiological-Clinical Etiological CHUPB

Results of intrauterine inseminations with two pooled sequential ejaculates in cases of oligozoospermia

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Asian Journal of Andrology 2018年第5期20卷 523-524页

作者： Jessika Moreau Nicolas Gatimel jean Parinaud roger Leandri Department of Reproductive Medicine Toulouse University Hospital 330 Avenue de Grande Bretagne (Great Britain Avenue) 31059 Toulouse France EA 3694 Human Fertility Research Group Toulouse University Hospital 330 Avenue de Grande Bretagne (Great Britain Avenue) 31059 Toulouse France

Dear Editor, Intrauterine insemination （IUI） is mainly indicated in cases of unexplained or mild male subfertility. In these cases, gonadotropin ovarian stimulation combined with gonadotropin-releasing hormone （GnRH） antagonist IUI leads to up to an 18% delivery rate per attempt.1 However, when the number of motile spermatozoa inseminated is lower than 1× 10^6, the success rate drops below 5%.1 Since semen quality varies intra-individually, this threshold may not be reached on the day of IUI. In such cases, some authors have suggested asking men to provide two consecutive ejaculates and to perform IUI with the pooled spermatozoa.2 However, the effectiveness of IUI with pooled ejaculates is not dear3.

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