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In this manuscript, we focus on the application of recently developed analytical scheme, namely, the rational sine-Gordon expansion method (SGEM). Some new exact solutions of Riemann wave system and the nonlinear Gross−Pitaevskii equation (GPE) by using this method are extracted. This method is based on the general properties of the SGEM which uses the fundamental properties of trigonometric functions. Many novel analytical solutions such as dark, bright, mixed dark–bright, hyperbolic, and periodic wave solutions are successfully extracted. Physical meanings of solutions are simulated by the various figures in 2D and 3D along with the contour graphs. Strain conditions of the existence are also reported in detail. Finally, modulation instability analysis of the nonlinear GPE is studied in detail. [ABSTRACT FROM AUTHOR]

The existence of factor and fractional factor in network graph in various settings has raised much attention from both mathematicians and computer scientists. It implies the availability of data transmission and network segmentation in certain special settings. In our paper, we consider P ≥ 2 -factor and P ≥ 3 -factor which are two special cases of general H -factor. Specifically, we study the existence of these two kinds of path factor when some subgraphs are forbidden, and several conclusions on the factor-deleted graph, factor critical-covered graph, and factor uniform graph are given with regards to network parameters. Furthermore, we show that these bounds are best in some sense. [ABSTRACT FROM AUTHOR]

This article investigates the new results of three nonlinear conformable models (NLCMs). To study such varieties of new soliton structures, we perform the generalized Kudryashov (GK) method. The obtained new results are defined in the styles of the exponential and rational functions. The derived new soliton structures are stable, serviceable, and fitting to embrace the conformable dynamics, chaotic vibrations, global bifurcations, optimal control problems, fluid mechanics, plasma physics, system identification, local bifurcations, control theory and resonances, and so many. The outcomes declare that the process is hugely valuable and accessible for investigating nonlinear conformable order models treated in theoretical physics. [ABSTRACT FROM AUTHOR]

This research paper focuses on the application of the tanh function method to find the soliton solutions of the (2+1)-dimensional nonlinear electrical transmission line model. Materials used to form a transmitting line are very important to transmit electric charge. In this sense, we find some new voltage behaviors such as dark, trigonometric, and complex function solutions. Choosing some suitable values of parameters, we present some various surfaces of results obtained in this paper. These results play an important role in telecommunications lines used to stand for wave propagations. [ABSTRACT FROM AUTHOR]

The stomach is usually considered as a hollow muscular sac, which initiates the second segment of digestion. It is the most sophisticated endocrine structure having unique biochemistry, physiology, microbiology, and immunology. The pivotal aim of the present study is to propose the nonlinear mathematical model of the nervous stomach system based on three compartments namely, tension (T), food (F), and medicine (M). The detailed description of each compartment is provided along with the mathematical form and different rates/factors, such as sleep factor, food rate, tension rate, medicine term, and death rate. The solution of the designed model is presented numerically by using the well-known differential transformation technique. The behavior of the obtained solution has been captured with respect to time as well as presentations of the numerical simulations. [ABSTRACT FROM AUTHOR]