ABSTRACT
This article delves into examining exact soliton solutions within the context of the generalized nonlinear Schrödinger equation. It covers higher-order dispersion with higher order nonlinearity and a parameter associated with weak nonlocality. To tackle this equation, two reputable methods are harnessed: the sine-Gordon expansion method and the [Formula: see text]-expansion method. These methods are employed alongside suitable traveling wave transformation to yield novel, efficient single-wave soliton solutions for the governing model. To deepen our grasp of the equation's physical significance, we utilize Wolfram Mathematica 12, a computational tool, to produce both 3D and 2D visual depictions. These graphical representations shed light on diverse facets of the equation's dynamics, offering invaluable insights. Through the manipulation of parameter values, we achieve an array of solutions, encompassing kink-type, dark soliton, and solitary wave solutions. Our computational analysis affirms the effectiveness and versatility of our methods in tackling a wide spectrum of nonlinear challenges within the domains of mathematical science and engineering.
Subject(s)
Nonlinear Dynamics , Models, Theoretical , Algorithms , Computer SimulationABSTRACT
This research paper focuses on the study of the (3+1)-dimensional negative order KdV-Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation, an important nonlinear partial differential equation in oceanography. The primary objective is to explore various solution techniques and analyze their graphical representations. Initially, two wave, three wave, and multi-wave solutions of the negative order KdV CBS equation are derived using its bilinear form. This analysis shed light on the behavior and characteristics of the equation's wave solutions. Furthermore, a bilinear Bäcklund transform is employed by utilizing the Hirota bilinear form. This transformation yields exponential and rational function solutions, contributing to a more comprehensive understanding of the equation. The resulting solutions are accompanied by graphical representations, providing visual insights into their structures. Moreover, the extended transformed rational function method is applied to obtain complexiton solutions. This approach, executed through the bilinear form, facilitated the discovery of additional solutions with intriguing properties. The graphical representations, spanning 2D, 3D, and contour plots, serve as valuable visual aids for understanding the complex dynamics and behaviors exhibited by the equation's solutions.
Subject(s)
Algorithms , Audiovisual AidsABSTRACT
Dengue is a mosquito-borne flaviviral serious febrile illness, most common in the tropical and subtropical regions including Pakistan. Vitamin D is a strong immunomodulator affecting both the innate and adaptive immune responses and plays a pivotal role in pathogen-defense mechanisms. There has been considerable interest in the possible role of vitamin D in dengue viral (DENV) infection. In the present prospective cross-sectional study, we assessed a possible association between serum vitamin D deficiency (VDD) and susceptibility towards severe dengue fever (DF) illness. Serum vitamin D levels were measured at the time of hospitalization in 97 patients diagnosed with dengue fever (DF), dengue hemorrhagic fever (DHF) or dengue shock syndrome (DSS) at Mayo Hospital, King Edward Medical University, Lahore, PK, from 16 November 2021 to 15 January 2022. In terms of disease severity, 37 (38.1%) patients were DF, 52 (53.6%) were DHF grade 1 and 2, and 8 (8.2%) were DSS. The results revealed that most patients (75 (77.3%)) were vitamin-D-deficient (i.e., serum level < 20 ng/mL), including 27 (73.0%) in DF, 41 (78.8%) in DHF grade 1 and 2, and 7 (87.5%) in DSS. The degree of VDD was somewhat higher in DSS patients as compared to DF and DHF grade 1 and 2 patients. Overall, serum vitamin D levels ranged from 4.2 to 109.7 ng/mL, and the median (IQR) was in the VDD range, i.e., 12.2 (9.1, 17.8) ng/mL. Our results suggest that there may be a possible association between VDD and susceptibility towards severe dengue illness. Hence, maintaining sufficient vitamin D levels in the body either through diet or supplementation may help provide adequate immune protection against severe dengue fever illness. Further research is warranted.
