Author: Anwar Ja'afar Mohamad Jawad

This paper retrieves soliton solutions to Kaup–Newell’s equation in optical fibers. Two fundamental integration schemes, namely the csch-function method and traveling wave hypothesis, obtain singular and bright soliton solutions respectively. The existence criteria for these solitons are also presented. DOI : https://www.sciencedirect.com/science/article/abs/pii/S0030402619300506

In this paper, we established a traveling wave solution by using the proposed Tan-Cot function algorithm for nonlinear partial differential equations. The method is used to obtain new solitary wave solutions for various type of nonlinear partial differential equations such as, the (2+1) – dimensional nonlinear Schrödinger equation, Gardner equation, the modified KdV equation, perturbed Burgers equation, general Burger’s-Fisher equation, and Benjamin-Bona-Mahony equation ,which are the important Soliton equations. Proposed method has been successfully implemented to establish new solitary wave solutions for the nonlinear PDEs. DOI : https://d1wqtxts1xzle7.cloudfront.net/32374222/2012_5_studies_in_mathematical_sciences-libre.pdf?1391496170=&response-content-disposition=inline%3B+filename%3DNew_Exact_Solutions_of_Nonlinear_Partial.pdf&Expires=1712137910&Signature=NPFjPY8U9Esa7c2cNoN9ljrAkIG7hxusbIXcxMew0l3uQhaC46yiiQmWrb8wAf3U4SYCL8darTlVWhxRqY2SB36-YVHDSCEcuxj940kDMppusHYttjYzchg2GkD3b6ChFHwhzvv0BfHDcgJ4sz-smMo13u6Z-24ziwsPeYFU-xBVzovKUvc0SC7hGEwzX9QfDhxca-WbO9tS~4lD7YJlkdw2pJ5Gj3Ywbjaa1N-nflPDWieNkmZPI8f2D~Qgnwu0svgAjL7YI7vfDCTROB3BeOILT5m7JzBqTmZuqfmfbk9VUi97cYdpx9ioNog~Oi~1ykJAuGkKzqDx1oc30HLtpw__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA

This paper obtains the solitary wave solutions of two different forms of Boussinesq equations that model the study of shallow water waves in lakes and ocean beaches. The tanh method is applied to solve the governing equations. The travelling wave hypothesis is also utilized to solve the generalized case of coupled Boussinesq equations, and, thus, an exact 1-soliton solution is obtained. The results are also supported by numerical simulations. DOI : https://www.sciencedirect.com/science/article/pii/S1026309812002945

This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV–Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method. DOI : https://repository.ruc.edu.iq/submit-an-article/

This paper employed three integration schemes to obtain soliton solutions in optical fibers with anti-cubic nonlinearity. These are traveling waves, tanh-coth scheme and finally the modified simple equation method. These yielded bright solitons, singular solitons, dark-singular combo solitons and other waves. The existence criteria for these solitons are presented. The paper concludes with a discussion on conservation laws. DOI : https://www.sciencedirect.com/science/article/abs/pii/S0749603617301362

This paper applies exp-function expansion algorithm to secure to cubic-quartic dark and singular optical solitons in birefringent fibers that are studied with four forms of nonlinear refractive index. These solitons are listed along with their existence criteria and are also classified. DOI : https://www.sciencedirect.com/science/article/pii/S2211379719334898

The Schrödinger–Hirota equation governs the propagation of optical solitons in a dispersive optical fiber. In this paper, this equation will be solved by the ansatz method for bright and dark 1-soliton solution. The power law nonlinearity will be assumed. By using the tanh method, some additional solutions will be derived. Finally, the numerical simulations will be given. DOI : https://www.sciencedirect.com/science/article/abs/pii/S0030399212000837

This paper reflects the implementation of a reliable technique which is called modified simple equation method (MSEM) for solving evolution equations. The proposed algorithm has been successfully tested on two very important evolution equations namely Fitzhugh–Nagumo equation and Sharma–Tasso–Olver equation. Numerical results are very encouraging. DOI : https://www.sciencedirect.com/science/article/abs/pii/S0096300310007150