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MULTI-SOLITON SOLUTIONS TO THE K-P EQUATION OF TENTH ORDER | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 دی 1403 اصل مقاله (548.05 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2024.56556.2366 | ||
| نویسندگان | ||
| Bharatha Kalegowda* 1؛ Rangarajan Raghavachar2 | ||
| 1PG Department of Mathematics, PG Studies and Research Centre, St. Philomena's College, Mysuru-570 015, India. | ||
| 2Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysuru-570 006, India. | ||
| چکیده | ||
| K-P equation is an important (2+1) - dimensional nonlinear PDE which has not only multi-solitons but also has complete integrability. In order to describe the long waves that propagates with weak dispersion in the direction of additional spatial variable y, Kadomstev and Petviashili formulated this model. In the literature, many researchers are interested to propose and work on higher order nonlinear PDE's possessing multi-solitons. Two powerful methods employed by researchers are Hirota's method to obtain multi-solitons and tanh-coth method to obtain one soliton solutions. In our work, K-P equation of order ten is derived and using Hirota's method, its multi solitons are worked out. The derived equation is also treated with the tanh method. This article emphasizes few bounded solutions to the equation in context. The main aim of the paper is to demonstrate the generalization of the K-P equation using Hirota operators and to study corresponding multi-solitons. We discuss few open problems for the proposed tenth order K-P equation. | ||
| کلیدواژهها | ||
| Higher order KP equation؛ the Hirota's bilinear method؛ the tanh method | ||
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