On Soliton Solutions of Perturbed Boussinesq and KdV-Caudery-Dodd-Gibbon Equations

Nonlinear science is a fundamental science frontier that includes research in the common properties of nonlinear phenomena. This article is devoted for the study of new extended hyperbolic function method (EHFM) to attain the exact soliton solutions of the perturbed Boussinesq equation (PBE) and KdV–Caudery–Dodd–Gibbon (KdV-CDG) equation. We can claim that these solutions are new and are not previously presented in the literature. In addition, 2d and 3d graphics are drawn to exhibit the physical behavior of obtained new exact solutions.

Optical singular and dark solitons to the nonlinear Schrodinger equation in magneto-optic waveguides with anti-cubic nonlinearity.

The present paper aims to investigate the coupled nonlinear Schrodinger equation (NLSE) in magneto-optic waveguides having anti-cubic (AC) law nonlinearity. The solitons secured to magneto-optic waveguides with AC law nonlinearity are extremely useful to fiber-optic transmission technology. Three constructive techniques, namely, the (G'/G)-expansion method, the modified simple equation method (MSEM), and the extended tanh-function method are utilized to find the exact soliton solutions of this model. Consequently, dark, singular and combined dark-singular soliton solutions are obtained. The behaviours of soliton solutions are presented by 3D and 2D plots.

New optical soliton solutions via two distinctive schemes for the DNA Peyrard–Bishop equation in fractal order

The deoxyribonucleic acid (DNA) dynamical equation, which emerges from the oscillator chain known as the Peyrard–Bishop (PB) model for abundant optical soliton solutions, is presented, along with a novel fractional derivative operator. The Kudryashov expansion method and the extended hyperbolic function (HF) method are used to construct novel abundant exact soliton solutions, including light, dark, and other special solutions that can be directly evaluated. These newly formed soliton solutions acquired here lead one to ask whether the analytical approach could be extended to deal with other nonlinear evolution equations with fractional space–time derivatives arising in engineering physics and nonlinear sciences. It is noted that the newly proposed methods’ performance is most reliable and efficient, and they will be used to construct new generalized expressions of exact closed-form solutions for any other NPDEs of fractional order.

New Exact Soliton Solutions of the ( 3 + 1 )-Dimensional Conformable Wazwaz–Benjamin–Bona–Mahony Equation via Two Novel Techniques

In this work, the ( 3 + 1 )-dimensional Wazwaz–Benjamin–Bona–Mahony equation is formulated in the sense of conformable derivative. Two novel methods of generalized Kudryashov and exp − φ ℵ are investigated to obtain various exact soliton solutions. All algebraic computations are done with the help of the Maple software. Graphical representations are provided in 3D and 2D profiles to show the behavior and dynamics of all obtained solutions at various parameters’ values and conformable orders using Wolfram Mathematica.