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Analyzing lumps, manifold periodic, interactions and rogue wave solutions for Klein-Gordon equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 مرداد 1405 اصل مقاله (14.13 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.66274.3087 | ||
| نویسندگان | ||
| Jamila Habib؛ Jamshad Ahmad* | ||
| Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat 50700, Pakistan. | ||
| چکیده | ||
| In present article, we discourse the problem of solving the non-linear Klein-Gordon equation to understand the wave dynamics in numerous physical systems. This famous mathematical model has significant practical applications, particularly in optics, quantum mechanics, solid state physics and cosmology. The purpose of this work is to analyze various lumps, breathers and interaction solutions to the renowned non-linear Klein-Gordon equation (KGE) via Hirota bilinear method. In particular, we obtain lump solution, lump one stripe, lump two stripe, lump periodic solution, manifold periodic solution, rogue wave solution, Ma breather and its relating rogue wave and Kuznetsov-Ma breather and its relating rogue wave for the proposed model. Furthermore, we have also shown interaction between lump, periodic and kink-wave. To calculate these solutions, the symbolic software Mathematica is used. The obtained solutions are demonstrated by generating two-dimensional, three dimensional, contour and density graphs. The results obtained appear as a noteworthy participation to the scientific world, providing a wide range of applications in many fields of science and technology. Hirota bilinear method appears as one of the most effective tools for constructing such solutions to various non-linear partial differential equations. This technique is authentic and simple for calculating several solutions to the proposed mathematical model. The study highlights the remarkable features of the applied method and its ability to handle various other mathematical models. | ||
| کلیدواژهها | ||
| Hirota bilinear method؛ Klein-Gordon equation؛ lumps؛ manifold periodic solution؛ rogue wave solution | ||
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