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The nonlinear Schrödinger equation (NLSE) is a fundamental equation in the field of nonlinear optics and plays an important role in the study of many physical phenomena. The present study introduces a new model that demonstrates the novelty of the paper and provides the advancement of knowledge in the area of nonlinear optics by solving a challenging problem known as the extended (3 + 1)-dimensional nonlinear conformable Kudryashov's equation (CKE) with generalized anti-cubic nonlinearity, which is a generalization of the NLSE to three spatial dimension and one temporal dimension for the first time. This work is significant because it advances our understanding of nonlinear optics and its applications to solve complex equations in physics and related disciplines. The extended hyperbolic function method (EHFM) and Nucci's reduction method are applied to the extended (3 + 1)-dimensional nonlinear CKE with generalized anti-cubic nonlinearity. The equation is solved by using the concept of conformable derivative, a recently developed operator in fractional calculus, which has advantages over other fractional derivatives in terms of accuracy and flexibility. The attained solutions include periodic singular, dark 1-soliton, singular 1-soliton, and bright 1-soliton which are visualized using 3D and contour plots. This study highlights the potential of using conformable derivative and the applied techniques to solve complex nonlinear differential equations in various fields. The obtained solutions and analysis will be useful in the design and analysis of optical communication systems and other related fields. Overall, this study contributes for the understanding of the dynamics of the extended (3+1)-dimensional nonlinear CKE and offers new insights into the use of mathematical techniques to tackle complex problems in physics and related fields. [ABSTRACT FROM AUTHOR]

The purpose of this work is to seek various innovative exact solutions using the new Kudryashov approach to the nonlinear partial differential equations (NLPDEs). This technique obtains novel exact solutions of soliton types. Moreover, several 3D and 2D plots of the higher dimensional Klein-Gordon, Kadomtsev-Petviashvili, and Boussinesq equations are demonstrated by considering the relevant values of the aforementioned parameters to exhibit the nonlinear wave structures more adequately. The new Kudryashov technique is an effective, and simple technique that provides new generalized solitonic wave profiles. It is anticipated that these novel solutions will enable a thorough understanding of the development and dynamic nature of such models. [ABSTRACT FROM AUTHOR]

In this work, a generalized (G ′ / G) -expansion method has been used for solving the nonlinear Chen–Lee–Liu equation. This method is a more common, general, and powerful mathematical algorithm for finding the exact solutions of nonlinear partial differential equations (NPDEs), where G = G (τ) follows the Jacobi elliptic equation [ G ′ (τ) ] 2 = H (G) , and we let H (G) be a fourth-order polynomial. Many new exact solutions such as the hyperbolic, rational, and trigonometric solutions with different parameters in terms of the Jacobi elliptic functions are obtained. The distinct solutions obtained in this paper clearly explain the importance of some physical structures in the field of nonlinear phenomena. Also, this method deals very well with higher-order nonlinear equations in the field of science. The numerical results described in the plots were obtained by using Maple. [ABSTRACT FROM AUTHOR]

This paper presents an analytical treatment of the perturbed nonlinear Schrödinger equation (P-NLSE) using the Lie symmetry method. The NLSE is a fundamental equation in nonlinear optics and describes the propagation of optical pulses in a nonlinear medium. In the presence of perturbations, the solution to the NLSE becomes more complicated and requires more sophisticated mathematical techniques to analyze. The Lie symmetry method is a powerful tool for finding exact solutions to nonlinear differential equations and has been applied successfully to a wide range of problems in physics and engineering. In this paper, we use the Lie symmetry method to obtain exact analytical solutions for the P-NLSE and study their properties. Our results show that the perturbations can have a significant effect on the behavior of the optical pulses, leading to phenomena such as soliton fission and dispersive shock waves. The Lie symmetry method is used to derive three generators for the Lie algebra, and two reductions are examined through combinations of vector generators. The Improved generalized Riccati equation and Nucci reduction method are then employed to obtain exact solutions, including bright soliton, multiple singular soliton, and exponential solutions. [ABSTRACT FROM AUTHOR]

This paper focuses on the use of the Sardar sub-equation method to obtain optical solitons for a nonlinear model that incorporates Kudryashov's quintuple power law and dual-form nonlocal nonlinearity. The model studies the propagation of pulses in optical fibers and the proposed technique is used to investigate various types of solitons including bright, dark, singular, periodic, combined dark-bright, and combined dark-singular solitons. The proposed technique is highly efficient and can also be utilized to solve higher-order nonlinear partial differential equations in fields such as fluid mechanics, plasma physics, and fiber optics. The paper includes a comparative analysis of the model and presents graphical representations for some of the obtained solutions. [ABSTRACT FROM AUTHOR]