Search

In this article, we will present new and more general traveling‐wave solutions for the Dodd–Bullough–Mikhailov equation based on the extended Fan sub‐equation method. The two‐dimensional affine sphere's intrinsic geometry is determined by Dodd–Bullough in the three‐dimensional unimodular affine space. The most significant accomplishment of our method is that we are able to provide all forms of the previously obtained solutions in one action, using at least four different approaches. As a result, the general elliptic equation with five parameters can be connected to other sub‐equations with three parameters that already exist, such as the Riccati equation, the first sort of elliptic equation, the auxiliary ordinary equation, and the modified Riccati equation. The extended Fan sub‐equation method is utilized to construct traveling‐wave solutions, solitary wave solutions, dark soliton solutions, and bell soliton solutions for the nonlinear Dodd–Bullough–Mikhailov equation. Mathematica is utilized to depict the dynamics of various wave structures in 3D, 2D, and contour formats, utilizing a specific set of parameters. Our graphical comparative analysis suggests that the employed method is both reliable and powerful for obtaining exact solutions of nonlinear evolution equations. The approach employed in this study may also be applicable in enhancing the understanding of numerous other complex physical phenomena. [ABSTRACT FROM AUTHOR]

The most important physical structure that is assumed to illustrate the geometry of optical soliton replication in optical fiber theory is the nonlinear Schrödinger equation (NLSE). Optical soliton generation in nonlinear optical fibers is a topic of great contemporary interest because of the numerous applications of ultrafast signal routing systems and short light pulses in communications. This analysis's main goal is to create a large number of soliton solutions for the dynamical model using a variety of contemporary analytical methods. This paper studies different soliton solutions to the perturbed NLSE with Kerr law nonlinearity using two sets of two distinct integration strategies: the mapping approach and the unified auxiliary equation method. The majority of solutions have been found as Jacobi elliptic functions with limiting ellipticity modulus values. Solitons like dark, bright, optical, lonely, and others are also retrieved. We were able to create various single‐type solutions with the help of these strategies. As a result, there is a variety of optical, bell‐shaped, single periodic, and multi‐periodic solutions. In order to validate the computations, the stability of the acquired findings must also be proven. The study provides a highly stunning and suitable strategy for combining numerous exciting wave demonstrations for more advanced models of the present era. Furthermore, we can assert that the outcomes reported here are unique and novel. [ABSTRACT FROM AUTHOR]

The generalized Korteweg–de Vries–Zakharov–Kuznetsov model is one of the dominant nonlinear complex structures to exhibit the influence of magnetic fields on weak ion‐acoustic waves in plasma made up of cool and hot electrons. In this study, the nonlinear higher dimensional model is subjected to the extended F$$ F $$‐expansion approach and the exp(−ϕ(ζ))$$ \exp \left(-\phi \left(\zeta \right)\right) $$‐expansion strategy in order to discover some novel traveling waves solutions and other exact solutions. There have been several solutions discovered, such as bright, dark, periodic, bell‐shaped, and single bell‐shaped wave structures. Furthermore, the stability analysis of the model is also reported along with the dynamical visualization of the charismatic behavior of various solitons with the aid of 3D, 2D, and contour plots. The proposed techniques can also be implemented to analyze a wide range of nonlinear evolution models emerging in diverse disciplines of science and technology including mathematical physics and plasma physics. [ABSTRACT FROM AUTHOR]