Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Articles Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Novel approaches for nonlinear Sine-Gordon equations using two efficient techniques Subject The topic of the resource Clique-polynomials; Functional matrix; q-homotopy analysis transform method Description An account of the resource In this work, we obtained a new functional matrix using Clique-polynomials of complete graphs (Formula presented.) with (Formula presented.) vertices and considered a new approach to solving the SineGordon (SG) equation. The clique polynomial method transforms this equation into a system of algebraic equations. The solution will be drawn with the help of Newton Raphsons method. Also, we employed the q-homotopy analysis transform method (q-HATM), which is the proper collision of the Laplace transform and the q-homotopy analysis method (q-HAM). To witness the reliability and accuracy of the considered schemes, some illustrations of the SG equation and double SG equation are considered. Here, the SG equation is solved easily and elegantly without using discretization or transformation of the equation by using the q-HATM. Also, in q-HATM, the presence of homotopy and axillary parameters allows us to have a large convergence region. The 3D surfaces of acquired solutions are drawn effectively. The tables of error analysis demonstrate the success of these methods. 2024 Informa UK Limited, trading as Taylor &amp; Francis Group. Creator An entity primarily responsible for making the resource S K.; Veeresha P.; Prakasha D.G.; Malagi N.S.; Ramane H.S.; Pise K.S. Source A related resource from which the described resource is derived International Journal of Modelling and Simulation Publisher An entity responsible for making the resource available Taylor and Francis Ltd. Date A point or period of time associated with an event in the lifecycle of the resource 2024-01-01 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1080/02286203.2024.2400658" target="_blank" rel="noreferrer noopener">https://doi.org/10.1080/02286203.2024.2400658</a> <br /><br /><a href="https://www.scopus.com/inward/record.uri?eid=2-s2.0-85205563412&amp;doi=10.1080%2F02286203.2024.2400658&amp;partnerID=40&amp;md5=36655de9e74d6faa1cfb5586c4643cf9" target="_blank" rel="noreferrer noopener">https://www.scopus.com/inward/record.uri?eid=2-s2.0-85205563412&amp;doi=10.1080%2f02286203.2024.2400658&amp;partnerID=40&amp;md5=36655de9e74d6faa1cfb5586c4643cf9</a> Rights Information about rights held in and over the resource Restricted Access Relation A related resource ISSN: 2286203; CODEN: IMSIE Format The file format, physical medium, or dimensions of the resource Online Language A language of the resource English Type The nature or genre of the resource Article Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant S K., Department of Mathematics, Bangalore University, Bengaluru, India; Veeresha P., Department of Mathematics, Christ University, Bangalore, India; Prakasha D.G., Department of Mathematics, Davangere University, Davangere, India; Malagi N.S., Department of Mathematics, Jain College of Engineering and Research, Belagavi, Karnataka, India; Ramane H.S., Department of Mathematics, Karnatak University, Dharwad, India; Pise K.S., Department of Mathematics, Karnatak University, Dharwad, India