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In this article, the sine-Gordon expansion method is employed to find some new traveling wave solutions to the nonlinear Schrödinger equation with the coefficients of both group velocity dispersion and second-order spatiotemporal dispersion. The nonlinear model is reduced to an ordinary differential equation by introducing an intelligible wave transformation. A set of new exact solutions are observed corresponding to various parameters. These novel soliton solutions are depicted in figures, revealing the new physical behavior of the acquired solutions. The method proves its ability to provide good new approximate solutions with some applications in science. Moreover, the associated solution of the presented method can be extended to solve more complex models.

In this study, the efficiency of the exponential rational function method for the new Hamiltonian amplitude equation has been investigated and the results have been graphically tested and analyzed using Mathematica software techniques. What is important is the high efficiency and accuracy of this method and the variety of answers that provide us with a wide range of answers. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation (NLSE) is a fundamental equation in the field of nonlinear optics and plays an important role in the study of many physical phenomena. The present study introduces a new model that demonstrates the novelty of the paper and provides the advancement of knowledge in the area of nonlinear optics by solving a challenging problem known as the extended (3 + 1)-dimensional nonlinear conformable Kudryashov's equation (CKE) with generalized anti-cubic nonlinearity, which is a generalization of the NLSE to three spatial dimension and one temporal dimension for the first time. This work is significant because it advances our understanding of nonlinear optics and its applications to solve complex equations in physics and related disciplines. The extended hyperbolic function method (EHFM) and Nucci's reduction method are applied to the extended (3 + 1)-dimensional nonlinear CKE with generalized anti-cubic nonlinearity. The equation is solved by using the concept of conformable derivative, a recently developed operator in fractional calculus, which has advantages over other fractional derivatives in terms of accuracy and flexibility. The attained solutions include periodic singular, dark 1-soliton, singular 1-soliton, and bright 1-soliton which are visualized using 3D and contour plots. This study highlights the potential of using conformable derivative and the applied techniques to solve complex nonlinear differential equations in various fields. The obtained solutions and analysis will be useful in the design and analysis of optical communication systems and other related fields. Overall, this study contributes for the understanding of the dynamics of the extended (3+1)-dimensional nonlinear CKE and offers new insights into the use of mathematical techniques to tackle complex problems in physics and related fields. [ABSTRACT FROM AUTHOR]

The increasing capabilities of control systems, driven by abundant data and computational resources, necessitate the incorporation of data‐based techniques with model‐based approaches. While mathematical models exist for air and space vehicles, they may not fully meet the requirements for expanding control system capabilities. Consequently, the development of data‐based extensions in collaboration with these models becomes crucial to provide specific analysis and synthesis tools in the hybrid realm for practical cases. This article introduces the data‐assisted control (DAC) framework for aerospace vehicles, with the NASA generic transport model serving as the platform for study. By leveraging data, the model‐based controller enhances performance during a damage event. Real‐time decisions are made to update the control law based on information obtained from the data, while the model‐based controller may not exhibit consistent performance. The closed‐loop system is shown to be stable in the transition phase between the data and the model, and robust against uncertainties. The dual unscented Kalman filter is employed to estimate fixed dynamic parameters and generalized force‐moment, and the Koopman estimator is used to estimate the evolution equation of the estimated forces and moments. The dual estimation model ensures observability by considering the persistency of excitation. Simulations have shown that the purely model‐based robust control leads to degradation of the closed‐loop performance in case of damage, suggesting the need for data assistance. The DAC framework offers a robust approach to integrate data and models, significantly enhancing control performance in practical aerospace applications. [ABSTRACT FROM AUTHOR]

This article studies a complex hyperbolic Schrodinger dynamical equation that is associated with nonlinear media via ultra short pulse propagation. The modified simplest equation method is executed to construct complex solitary wave and other solutions of the aforesaid equation by considering it in conformable M-fractional derivative sense. The acquired solutions are in the form of solitary and periodic waves and rational functions. These solutions are also described with their graphical representations by assuming appropriate values of required parameters. Moreover, the results show that the aforesaid approach can be effiective for solving such nonlinear Schrodinger equations arising in nonlinear optics and physical sciences. [ABSTRACT FROM AUTHOR]

In this work, we consider the (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Solitary wave solutions, soliton wave solutions, elliptic wave solutions, and periodic (hyperbolic) wave rational solutions are obtained by means of the unified method. The solutions showed that this method provides us with a powerful mathematical tool for solving nonlinear conformable fractional evolution equations in various fields of applied sciences.

The aim of this paper is to investigate hyperbolic rational solutions of four conformable fractional Boussinesq-like equations using the method of exponential rational function (ERF). The present method is a good scheme, reveal distinct exact solutions and convenient for solving other types of nonlinear conformable fractional differential equations. These solutions are of significant importance in coastal and ocean engineering where the fractional Boussinesq-like equations modeled for some special physical phenomenon.