MULTI-SOLITON SOLUTIONS TO THE K-P EQUATION OF TENTH ORDER

Articles in Press

Document Type : Research Paper

Authors

1 PG Department of Mathematics, PG Studies and Research Centre, St. Philomena's College, Mysuru-570 015, India.

2 Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysuru-570 006, India.

Abstract

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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 19 January 2025

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History

  • Receive Date: 11 May 2023
  • Revise Date: 23 May 2024
  • Accept Date: 18 January 2025

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