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The main goal of this research work is to explore novel soliton solutions and dynamics of solitonic structures to asymmetric Nizhnik–Novikov–Veselov (ANNV) equations by two methods, namely, the generalized exponential rational function (GERF) method and the modified extended tanh expansion (METE) method. These techniques are the most effective and reliable tools for solving nonlinear equations with partial derivatives. The used methods provide a wide range of soliton solutions that can motivate applied scientists and researchers for these specific structures. These acquired solutions are in the form of exponential, trigonometric and hyperbolic functions including, tan , sin , sec , cot , csc , sinh , tanh , sech , cosh , coth , csch and of their combinations. It has also been observed that the obtained soliton solutions of the ANNV equations are bell-shape, anti-bell-shape, periodic solution, multisoliton and different types of soliton solutions. To illustrate the physical features and dynamics characteristics of some obtained solutions, three-dimensional (3D) and two-dimensional (2D) figures are exhibited through the Mathematica software. The methods applied in this paper are suitable to study the soliton solutions for the ANNV equation without producing the complexities in some other known analytical method. Finally, the employed methods can be earmarked easily for solving various classes of nonlinear evolution equations appearing in mathematical physics, fluid dynamics, plasma physics, nonlinear waves and nonlinear sciences. [ABSTRACT FROM AUTHOR]

In this paper, we use two efficient mathematical approaches to obtain a variety of soliton solutions to the (3+1)-dimensional Schrödinger equation: the generalized Riccati equation mapping method and the newly proposed modified generalized exponential rational function method. These techniques extracted standard, illustrative, rich dynamical structures, and further comprehensive soliton solutions and traveling wave solutions involving hyperbolic form, trigonometric form, and exponential form. The obtained results have been verified by placing them back into the mentioned nonlinear partial differential equation via symbolic computation in Mathematica. Thereafter, the graphical demonstrations of some attained solutions are discussed for a better understanding of the physical phenomenon. We have portrayed the three-dimensional, contour plot, and two-dimensional graphs for different parametric values. The attained results demonstrate the generalized Riccati equation mapping method and modified generalized exponential rational function techniques for extracting soliton solutions to nonlinear partial differential equations are efficient, compatible, and reliable in nonlinear sciences, optical fibers, and engineering. [ABSTRACT FROM AUTHOR]

In this study, the improved (℘ ′ / ℘) expansion method and Exp a 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. [ABSTRACT FROM AUTHOR]