Exact Solutions for the Nonlinear PDE Describing the Model of DNA Double Helices using the Improved (G ′ /G)- Expansion Method

Abstract: The objective of this article is to apply the improved(G ′ /G)- expansion method for constructing many exact solutions with parameters of the nonlinear partial differential equation (PDE) describing the model of DNA double helices. The stretch of the hydrogen bonds is considered as a nonlinear chain with cubic and quadratic potential. When the parameters take special values, many solitary wave solutions and periodic wave solutions can be found. Comparison between some of our new results and the well-known results are given

( / ) G G �- Expansion Method to Traveling Wave Solutions of Two Nonlinear

The authors of the above article proposed the improved ( G� / G)- expansion method and found some traveling wave solutions for each of two nonlinear evolution equations in mathematical physics, namely the Regularized Long Wave (RLW) equation and the Symmetric Regularized Long Wave (SRLW) equation. In the present article, we have noted that if we use a suitable transformation, the improved (G’/G)expansion method can be reduced into the well-known generalized Riccati equation mapping method which provides us with much more traveling wave solutions, namely twenty seven solutions for each of these two nonlinear evaluation equations. Comparison between the results of these two methods is presented

Dispersive Optical Solitons to Stochastic Resonant NLSE with Both Spatio-Temporal and Inter-Modal Dispersions Having Multiplicative White Noise

The current article studies optical solitons solutions for the dimensionless form of the stochastic resonant nonlinear Schrödinger equation (NLSE) with both spatio-temporal dispersion (STD) and inter-modal dispersion (IMD) having multiplicative noise in the itô sense. We will discuss seven laws of nonlinearities, namely, the Kerr law, power law, parabolic law, dual-power law, quadratic–cubic law, polynomial law, and triple-power law. The new auxiliary equation method is investigated. We secure the bright, dark, and singular soliton solutions for the model

Highly Dispersive Optical Solitons in Fiber Bragg Gratings with Quadratic-Cubic Nonlinearity

Highly dispersive solitons in fiber Bragg gratings with quadratic-cubic law of nonlinear refractive index are studied in this paper. The G′/G-expansion approach and the enhanced Kudryashov’s scheme have made this retrieval possible. A deluge of solitons, that emerge from the two integration schemes, are presented

Highly Dispersive Optical Solitons in Fiber Bragg Gratings with Kerr Law of Nonlinear Refractive Index

This paper obtains highly dispersive optical solitons in fiber Bragg gratings with the Kerr law of a nonlinear refractive index. The generalized Kudryashov’s approach as well as its newer version makes this retrieval possible. A full spectrum of solitons is thus recovered