Two Mode Version of Hirota-Ramani Equation and its Abundant Soliton Structures

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Mersin University, Mersin, Turkey.

2 Department of Mathematics, Federal University, Dutse, Nigeria.

3 Department of Mathematics, Firat University, Elazığ, Turkey.

4 1. Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan.\\ 2. Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah, 64001, Iraq.

5 Department of Mathematics and Information Technologies, Tashkent State Pedagogical University, Tashkent, Uzbekistan.

6 Civil and Environmental Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.

Abstract

Wave propagation phenomena are connected to Hirota-Ramani equation (HRE) and as a member of the integrable
PDEs, the HRE is used in many different domains. Considering this, we employ Kursonky’s approach and
developed the two-mode or Dual-mode version of the HRE that describes the propagation of two-wave solitons
moving simultaneously in the same direction with mutual interaction that depends on an embedded phase-velocity
parameter. The existing studies explore single mode version of HRE whereas two mode version remain unexplored.
Motivated by this gap, we utilized the generalized Ricatti equation mapping method and the modified
extended tanh-function method to find the different soliton structures of the developed model. By using these
techniques we developed bright, dark, kink, anti-kink, singular and peakon shaped soliton solutions. Additionally,
we performed a stability analysis of the LGH equation using the linear stability approach. A back substitution
for each of the obtained result into the developed model was performed to ensure reliability and accuracy of the
obtained solutions. The 3D and 2D graphical representation of some of the obtained results were portrayed. The
efficacy and competence of the proposed methods in analyzing and obtaining soliton solutions for nonlinear partial
differential equations (NLPDEs) are demonstrated through their implementation in this work. Additionally,
the derived solutions are original and reflect contributions not previously documented in the literature.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 20 April 2026

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History

  • Receive Date: 07 August 2025
  • Revise Date: 10 December 2025
  • Accept Date: 14 April 2026

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