Abundant exact solutions for the deoxyribonucleic acid (DNA) model

Abstract

In this study, the improved [Formula: see text] expansion method and Exp[Formula: see text] function method are used to construct the newly closed-form exact solutions for the deoxyribonucleic acid (DNA) model which includes hyperbolic, trigonometric and exponential solutions. These solutions include a wealth of information regarding the dynamical behavior of homogeneous long elastic rods with circular cross-sections. These rods comprise a pair of polynucleotide rods of the DNA molecule that are connected by an elastic diaphragm, demonstrating the involvement of the hydrogen bond in this communication. The performance of these approaches demonstrates their use and efficacy in solving a variety of nonlinear evolution problems of integer and fractional order. The physical significance of the established and the obtained solutions has been shown via 3D shapes. It is worth noting that the solutions obtained here via the proposed schemes are more generalized and can be helpful to demonstrate the internal interaction of the DNA model arising in mathematical biology. The proposed method has been used to obtain exact traveling wave solutions for fraction nonlinear partial differential equations (NPDEs) arising in nonlinear sciences.

Analytical Soliton Solutions of the Coupled Radhakrishnan‐Kundu‐Lakshmanan Equation via Three Techniques

“…Solving this system, we get the following solution classes: Class 1: Substituting (40) in (38) with ( 11), (13), and (21), we obtain the following solution of (2): Class 2:…”

“…The theory and investigation of soliton solutions is one of the important research fields relating to nonlinear partial differential equations ascending in telecommunication engineering, optics, mathematical physics, and other domains of nonlinear sciences. Therefore, diverse academics and researchers developed a number of numerical and analytical techniques, namely, the ðm + 1/G ′ Þ-expansion technique [1], the truncated M-fractional derivative scheme [2], the q-homotopy analysis technique [3], Atangana-Baleanu operator scheme [4], the improved Bernoulli subequation function process [5], the sine-Gordon expansion approach [6], the Haar wavelet technique [7], the biframelet systems process [8], the Lie symmetry technique [9], the generalized exponential rational function mode [10], the Painlevé analysis [11], the extended subequation method [12], the improved ðG′/GÞ-expansion scheme [13], the Hirota simplified method [14], the onedimensional subalgebra system [15], Painlevé analysis and multi-soliton solutions technique [16], the one-parameter Lie group of transformations approach [17], etc.…”

New wave behaviors of the Fokas-Lenells model using three integration techniques

“…Consequently, mathematical physicists are highly interested in obtaining soliton solutions for nonlinear models [ 8 , 9 ]. Numerous well-known nonlinear structures exhibit the presence of soliton solutions, such as the Jimbo-Miwa-like model [ 10 ], the STOL model [ 11 ], the Sine-Gordon equation [ 12 ], the nonlinear Schrödinger equation [ 13 ], the Konopelchenko-Dubrovsky equation [ 14 , 15 ], the nonlocal Klein-Gordon model [ 16 ], the Wadati-Konno-Ichikawa equation [ 17 ], the phi-four model [ 18 ], the Gerdjikov-Ivanov equation [ 19 ], the deoxyribonucleic acid (DNA) model [ 20 ], the KdV-BBM equation [ 21 ], etc. Diverse effective methods exist for managing these nonlinear structures and deriving soliton solutions, such as the generalized exponential rational function technique [ 22 , 23 ], the generalized Riccati equation mapping scheme [ 24 ], the ð-dressing method [ 25 ], the extended sinh-Gordon equation approach [ 26 ], the Hirota bilinear technique [ 27 ], etc.…”