Complexiton and interaction solutions of the (1+1)-dimensional sixth-order Ramani equation

Sukri Khareng; Ömer Ünsal; Sukri Khareng; Ömer Ünsal

doi:10.3934/math.2025905

AIMS Mathematics

2025, Volume 10, Issue 9: 20262-20272. doi: 10.3934/math.2025905

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Complexiton and interaction solutions of the (1+1)-dimensional sixth-order Ramani equation

Sukri Khareng ,
Ömer Ünsal ^,

Eskişehir Osmangazi University, Department of Mathematics and Computer Sciences, Eskişehir, 26480, TÜRKİYE

Received: 11 June 2025 Revised: 19 August 2025 Accepted: 25 August 2025 Published: 04 September 2025
MSC : 35A25, 35C08, 35Q35, 76B15

This study shows the attainability of solutions to the sixth-order Ramani equation through a procedure called the simplified Hirota method, which can be thought of as a special case of the Hirota direct method. This special case comes into sight by virtue of the transition between real and complex parameters. In this procedure, dispersion relations and phase shifts play a decisive role in finding solutions. Particularly, chosen cases of phase shifts provide us different kinds of solutions, such as soliton, complexiton, and interaction solutions.
- complexiton solution,
- interaction solution,
- simplified Hirota method,
- the (1+1)-dimensional sixth-order Ramani equation
Citation: Sukri Khareng, Ömer Ünsal. Complexiton and interaction solutions of the (1+1)-dimensional sixth-order Ramani equation[J]. AIMS Mathematics, 2025, 10(9): 20262-20272. doi: 10.3934/math.2025905

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Abstract

This study shows the attainability of solutions to the sixth-order Ramani equation through a procedure called the simplified Hirota method, which can be thought of as a special case of the Hirota direct method. This special case comes into sight by virtue of the transition between real and complex parameters. In this procedure, dispersion relations and phase shifts play a decisive role in finding solutions. Particularly, chosen cases of phase shifts provide us different kinds of solutions, such as soliton, complexiton, and interaction solutions.

References

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