Roles of modified Chaplygin–Jacobi and Chaplygin–Abel gases in FRW universe

In this paper, we have considered flat Friedmann–Robertson–Walker (FRW) model of the universe and reviewed the modified Chaplygin gas as the fluid source. Associated with the scalar field model, we have determined the Hubble parameter as a generating function in terms of the scalar field. Instead of hyperbolic function, we have taken Jacobi elliptic function and Abel function in the generating function and obtained modified Chaplygin–Jacobi gas (MCJG) and modified Chaplygin–Abel gas (MCAG) equation of states, respectively. Next, we have assumed that the universe is filled in dark matter, radiation, and dark energy. The sources of dark energy candidates are assumed as MCJG and MCAG. We have constrained the model parameters by recent observational data analysis. Using [Formula: see text] minimum test (maximum likelihood estimation), we have determined the best-fit values of the model parameters by OHD[Formula: see text]CMB[Formula: see text]BAO[Formula: see text]SNIa joint data analysis. To examine the viability of the MCJG and MCAG models, we have determined the values of the deviations of information criteria like △AIC, △BIC and △DIC. The evolutions of cosmological and cosmographical parameters (like equation of state, deceleration, jerk, snap, lerk, statefinder, Om diagnostic) have been studied for our best-fit values of model parameters. To check the classical stability of the models, we have examined the values of square speed of sound [Formula: see text] in the interval [Formula: see text] for expansion of the universe.

Dispersive soliton solutions for the Salerno equation for the nonlinear discrete electrical lattice in the forbidden bandgaps

In this paper, the modified Jacobi elliptic function method is applied for Salerno equation which describes the nonlinear discrete electrical lattice in the forbidden bandgaps. Dark and bright solitons are obtained. Also, periodic solutions and periodic Jacobi elliptic function solutions are reported. Moreover, for the physical illustration of the obtained solutions, three-dimensional and two-dimensional graphs are presented.

Exact Solutions to the Nonlinear Schrödinger Equation with Time-Dependent Coefficients

In this paper, a trial function method is employed to find exact solutions to the nonlinear Schrödinger equations with high-order time-dependent coefficients. This system might be used to describe the propagation of ultrashort optical pulses in nonlinear optical fibers, with self-steepening and self-frequency shift effects. The new general solutions are found for the general case a 0 ≠ 0 including the Jacobi elliptic function solutions, solitary wave solutions, and rational function solutions which are presented in comparison with the previous ones obtained by Triki and Wazwaz, who only studied the special case a 0 = 0 .

Stability and Extraction of New Optical Wave Solutions of Cascaded System in (2 + 1)-dimensions

This paper uses the new modified sub-ODE method, the new extended auxiliary equation method, and the new Jacobi elliptic function expansion method to revisit the (2+1)-dimensional coupled nonlinear Schr¨odinger equation with cascading effect. As a consequence, dark, bright, kinkantikink, singular solitons, Weierstrass elliptic function, doubly periodic, and complex optical soliton solutions are retrieved. All solutions are described, along with the existence criterion on the parameters. As solitons are used for data transfer, the obtained results may be found usage in optical couplers, birefringed fibres, and optoelectronic devices. A comparison of the obtained results with those found in the literature is given. The dynamical behaviour of some of the obtained solutions has been explored for suitable choices of the parameters. Using the property of Hamiltonian systems, the solitons stability is determined.

Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method

In this manuscript, the space-time fractional Equal-width (s-tfEW) and the space-time fractional Wazwaz-Benjamin-Bona-Mahony (s-tfWBBM) models have been investigated which are frequently arises in nonlinear optics, solid states, fluid mechanics and shallow water. Jacobi elliptic function expansion integral technique has been used to build more innovative exact solutions of the s-tfEW and s-tfWBBM nonlinear partial models. In this research, fractional beta-derivatives are applied to convert the partial models to ordinary models. Several types of solutions have been derived for the models and performed some new solitary wave phenomena. The derived solutions have been presented in the form of Jacobi elliptic functions initially. Persevering different conditions on a parameter, we have achieved hyperbolic and trigonometric functions solutions from the Jacobi elliptic function solutions. Besides the scientific derivation of the analytical findings, the results have been illustrated graphically for clear identification of the dynamical properties. It is noticeable that the integral scheme is simplest, conventional and convenient in handling many nonlinear models arising in applied mathematics and the applied physics to derive diverse structural precise solutions.

Travelling wave solutions to the proximate equations for LWSW

By feat of Maple 17 and a subsidiary ordinary differential equation, a new extension algebraic method is chosen to construct the travelling wave solutions to the proximate equation set involving an arbitrary parameter for long waves over shallow-water. Multiple triangle periodic solutions and new Jacobi elliptic function solutions are obtained. This procedure is applicable to other nonlinear partial differential equations as well.

Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model

In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

New Solutions for the Generalized BBM Equation in terms of Jacobi and Weierstrass Elliptic Functions

The Jacobi elliptic function method is applied to solve the generalized Benjamin-Bona-Mahony equation (BBM). Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered. A power series method is also applied in some particular cases. Some solutions are expressed in terms of the Weierstrass elliptic function.