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In this work, the Hirota bilinear symbolic computational method along with test functions and the generalized exponential rational function method are capitalized to secure soliton and lump solutions to the Sharma–Tasso–Olver–Burgers equation. Several novel soliton solutions are observed in unique patterns such as periodic, exponential, hyperbolic, dark, singular, and combo forms. Additionally, we also extract interaction, lump and breather solutions of the governing model. The novel characteristic of this work is the attained results, which were not before computed. Modulation instability of the governing equation is also examined via linear stability theory. To demonstrate the physical aspects and configuration of the attained solitons, some distinct graphs are plotted in different shapes. The validity of the solutions is verified by using Mathematica. The constructed outcomes are very encouraging and entail that the concerned methods can be utilized to acquire assorted improved, innovative, and advantageous outcomes for miscellaneous remarkable nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

Understanding the intricate Korteweg–de Vries ( c K d V ) equation is paramount for comprehending various nonlinear wave phenomena, owing to its capacity to depict the propagation of nonlinear waves in media characterized by complex-valued dispersive and nonlinear coefficients. The practical ramifications of the c K d V equation are extensive, spanning disciplines such as optics, plasma physics, and other realms dealing with intricate media. This investigation employs the Khater II method and a generalized rational approach as analytical methodologies to generate novel exact solutions for the c K d V equation. The Khater II method is employed to transform the nonlinear partial differential equation into a nonlinear ordinary differential equation, thus facilitating a systematic resolution. Moreover, the generalized rational technique utilizes a rational ansatz function to derive diverse forms of solutions. Application of these methodologies leads to the discovery of fresh exact solutions, encompassing solitary and periodic wave solutions for the c K d V equation. These solutions are expressed in rational forms featuring arbitrary functions, thereby expanding the repertoire of known solutions for the model. The efficacy of the analytical methodologies employed becomes evident through the discovery of these novel exact solutions, thereby enriching our understanding of the physical interpretations and wave characteristics associated with the c K d V equation. The derived solutions augment the existing body of knowledge pertaining to the model. This research enhances our comprehension of the c K d V equation, thereby advancing nonlinear wave analysis with potential applications in physics, optics, plasma science, and allied engineering domains. Future investigations may explore the extension of these methodologies to address other nonlinear wave equations. [ABSTRACT FROM AUTHOR]

This study delves into investigating the stability of solutions pertaining to the generalized Davey–Stewartson ( D S ) equation by employing the generalized rational method and projective Riccati equations method within the Hamiltonian system framework. The central focus lies in unraveling the physical significance of this model within the realm of plasma physics, shedding light on its intricate connections with analogous equations. The generalized D S equation, a pivotal nonlinear evolution model, serves as a vital tool in comprehending the evolution of coupled waves across various physical systems, notably within the domains of fluid dynamics and plasma physics. Its significance lies in its capacity to elucidate the intricate interplay among different wave components, offering a holistic perspective on wave interactions within plasma mediums. Through the meticulous application of rigorous analytical methods, this investigation uncovers pivotal insights into the stability of solutions, thereby enriching our understanding of mathematical models in plasma physics. The findings presented in this research contribute significantly to advancing the understanding of nonlinear dynamics, with profound implications for future exploration in plasma physics and related fields. In essence, this study underscores the analytical prowess of the generalized rational and projective Riccati equations methods, accentuating their relevance and applicability to the generalized D S equation and, by extension, their role in enhancing our comprehension of coupled wave phenomena within diverse plasma systems. [ABSTRACT FROM AUTHOR]

This manuscript introduces a novel bidirectional wave dynamics to the q-deformed Sinh-Gordon model. The main objective of this study is to investigate the simultaneous motion of two symmetrical waves. The ϕ 6 -model expansion technique is used for achieving the required objective. The ϕ 6 -model expansion technique extracts new solitary wave solutions for the proposed model. Moreover, we delve into the mathematical aspects and explore the physical characteristics of the q-deformed Sinh-Gordon equation in its bidirectional form. The study provides intricate derivations of the innovative solutions, accompanied by visual representations that offer insights into their physical structures. The findings of this investigation significantly contribute to our comprehension of this model. Finally, fascinating three-dimensional plots and two-dimensional line plots are displayed. [ABSTRACT FROM AUTHOR]

In this paper the K-Nearest Neighbor (KNN) model which is one of machine learning (ML) algorithm is applied to distinguish between the four distinct Hermite Gaussian (HG) beams (HG00, HG01, HG02, and HG03) in mode division multiplexed (MDM)-free space optics (FSO) communication system. First, the performance of the FSO system using these different HG beams is investigated for rainy weather conditions in various Indian cities having distinct geographical locations. Transmission performance is evaluated in terms of quality (Q)-factor, signal-to-noise ratio (SNR), bit error rate (BER), and eye diagrams. Then, the values of the BER for the different HG beams are applied to the KNN ML model as to classify between them. HG modes are used for capacity enhancement. Results indicate that 80 Gbps can be transmitted over 1000 m in Hyderabad, 800 m in Pune, 580 m in Chennai, and 475 m in Mumbai at log (BER) ~ 10 - 15 , Q-factor less than 8, and SNR ~ 10 dB. Additionally, the K-Nearest Neighbor (KNN) ML model shows 94% classification accuracy between four HG beams. [ABSTRACT FROM AUTHOR]

In this paper, the perturbed Gerdjikov–Ivanov (GI) equation using a truncated M-fractional derivative is studied in mathematical nonlinear optics. We are explored its novel dark and other soliton solutions and compared them with the existing results. To obtain the objective, two particular methods, the modified extended tanh expansion method and the E x p a function method, are implemented. In this exercise, an arrangement of exact solitons is received as well as verified by utilizing the symbolic soft computations. The dynamical characteristics of the obtained results, along with a fractional parameter, are also discussed via two and three-dimensional graphs. These solutions are suggested that the employed methods are impressive, determined and smooth as compared to many other methods. The work of this paper is of high importance regarding its applications in photonic crystal fibers and mathematical physics. [ABSTRACT FROM AUTHOR]

Mode division multiplexing (MDM) is an emerging multiplexing technique that simultaneously transmits independent channels through a spatial light modulator (SLM). Further, Spectral amplitude coding optical code division multiple access (SAC-OCDMA) is an encouraging invention because it gives an appealing answer for burst and asynchronous environment. In addition, free space optics (FSO) provides a cost-effective, secure, high data rate for last mile access compared to other systems. In this paper, a hybrid 100 GB/s SACOCDMA-FSO-MDM system is proposed, and its performance is estimated by using four SAC-OCDMA codes that are Zero Cross Correlation (ZCC), Random Diagonal (RD), Multi Diagonal (MD), and Enhanced double weight (EDW) under atmospheric turbulences such as haze, rain, and clear weather. Laguerre Gaussian (LG) modes (used for MDM) and direct detection (DD) method are used for the construction of the system using 10 channels; each carries 10 Gb/s data. Results specify that the ZCC code is more suitable under all the atmospheric conditions as it possesses no cross-correlation, lesser noise that diminishes the hardware's complexity. For clear weather, the ZCC code gives a BER of 10–29 at a maximum distance of 22 km. [ABSTRACT FROM AUTHOR]

A new variable weight zero cross correlation code (VZCC) is designed that support different class of services in spectral encoding for OCDMA scheme. The proposed code has many benefits, such as the easy and strong mathematical way of code construction, acceptable code length, variable ZCC. A transmitter–receiver structure of the VZCC OCDMA system is presented. The performance of the proposed VZCC OCDMA system with noise sources at the direct detection scheme is studied using gaussian approximation. It is observed that the VZCC OCDMA scheme is able to accommodate more users in contrast to the reported techniques having a privilege of triple play services. For BER 10–9 the Modified Double Weight (MDW), Modified Quadratic Congruence (MQC), Modified Frequency Hopping (MFH), Hadamard, and VZCC supports 68, 70, 62, 18, and 145 users, respectively at − 10 dBm power. [ABSTRACT FROM AUTHOR]

Since last decade, Spectral Amplitude Coding Optical Code Division Multiple Access (SAC-OCDMA) system has become popular since it offers security, unlimited bandwidth and eliminates multiple access interference. On the other hand, Free Space Optics (FSO) provides last-mile access at a high data rate. We have designed a new zero cross-correlation code, which is named as an identity-type matrix ZCC code. The proposed code’s performance is evaluated by designing 120 GB/s Hybrid FSO-MDM (mode division multiplexing) and SAC-OCDMA system under atmospheric turbulence using the direct detection (DD) technique. Six channels, carrying 20 GB/s data each, are transmitted over the FSO channel. Two Laguerre Gaussian modes (LG 00 and LG 01) are used in MDM. The results of the simulation show that the performance of the proposed code is better in comparison to existing codes. [ABSTRACT FROM AUTHOR]