Cosmological behavior of a hyperbolic solution in f(Q) gravity

This article discusses the (2+1)-dimensional case of the Zakharov-Kuznetsov (ZK) equation. The (2+1)-dimensional ZK equation is primarily used to describe wave propagation phenomena in multi-dimensional media. In plasma, liquids, or gases, waves may be influenced by multiple elements. Due to nonlinear effects, the propagation speed, shape and interactions of these waves become complex. We have obtained a variety of exact solutions of the (2+1) dimensional ZK equation by using two effective methods: the improved extended tanh function method and the modified Kudryashov method. The forms of the solutions include exponential solutions, logarithmic solutions, hyperbolic solutions and trigonometric solutions. In addition, by selecting appropriate parameter values,we have plotted three-dimensional and two-dimensional images to illustrate the physical behavior of the exact solutions.

The time(T)- and time-space(TS)-fractional higher-order Schro ̈dinger(FHNLS) equations are stud- ied, which can describe the dispersion and nonlinearity of optical pulse propagating in nonuniform fiber systems. The generalized fractional wave transformation is appropriately used to convert the T- and TS-FHNLS equations into some ordinary differential equations, and the real and imaginary parts are separated respectively. A few of new exact analytical solutions with fractional parameters α and β are obtained with the homogeneous balance method, including time-fractional and time-space frac- tional bright and dark solutions, and some fractional order effects on soliton solutions are considered. Some dynamic behaviors of the hyperbolic soliton solutions of the fractional-typed sech and tanh are obtained, some novel forms of the dark solitary wave and bright solitary wave are presented with the parameters of α and β. And some novel toroidal, spherical bright and dark solitons are derived by the toroidal and spherical coordinate transformations. Further, the four kinds of time-space fractional non-autonomous soliton solutions of the higher-order Gross-Pitaevskii(GP) model are derived, we find that the value of α decreases, the number of oscillations or singularities increases for small time values and decreases for large time values. These results are significantly different from the classical higher-order nonlinear Schro ̈dinger and GP equations, which helps to understand the solitary wave transmission pattern and applies to the physical manipulation.

This paper focuses on the Davey–Stewartson (DS)-II equation, and the extended modified auxiliary equation mapping (EMAEM) architectonic is used to develop a new set of solutions such as kink, singular kink, rational, combined soliton-like solutions, bell-type solutions, trigonometric and hyperbolic solutions. Furthermore, this study reveals that the used technique is efficient for solving other nonlinear evolution equations (NLEEs). The Painleve test ([Formula: see text]-test) will also be used to examine the integrability of the DS-II equation. Finally, graphical simulations are designed to show the exact behavior of solutions as well as the efficacy of the suggested strategy.

Exact cosmological solutions from Hojman conservation quantities