Abstract
An effective and simple method to solve nonlinear evolution partial differential equations is the self-similarity transformation, in which one utilizes solutions of the known equation to find solutions of the unknown. In this paper, we employ an improved similarity transformation to transform the $$(2+1)$$-dimensional (D) sine-Gordon (SG) equation into the $$(1+1)$$-D SG equation and obtain non-rational solutions of the $$(2+1)$$-D SG equation by utilizing the known solutions of the $$(1+1)$$-D SG equation. Based on the solutions obtained, and with the help of special choices of the involved solution parameters, several localized structures of the $$(2+1)$$-D SG model are analyzed on a finite background, such as the embedded hourglass, split silo, dumbbell, and pie solitons. Their spatiotemporal profiles are displayed, and their properties are discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
