Multi-soliton solutions to the K-P equation of tenth-order

Kalegowda, Bharatha; Raghavachar, Rangarajan

doi:10.22034/cmde.2024.56556.2366

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	Multi-soliton solutions to the K-P equation of tenth-order
Computational Methods for Differential Equations
مقاله 26، دوره 14، شماره 2، تیر 2026، صفحه 919-928 اصل مقاله (594.16 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
Kadomtsev–Petviashvili (KP) 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 propagation weakly dispersive 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 PDEs possessing multi-solitons. Two powerful methods employed by researchers are Hirota's method to obtain multi-solitons and $\tanh-\coth$ method to obtain single-soliton solutions. In our work, a tenth-order generalization of the KP equation is derived and using Hirota's method, its multi-solitons are worked out. Furthermore, 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 this paper is to demonstrate the generalization of the K-P equation using Hirota operators and to study corresponding multi-solitons. Finally, some open problems related to the proposed tenth-order KP equation are discussed.
کلیدواژه‌ها
Higher order KP equation؛ The Hirota bilinear method؛ The $\tanh$ method

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Multi-soliton solutions to the K-P equation of tenth-order