Investigating novel soliton solutions and chaotic Structures for the (3+1)-dimensional fractional q-deformed tanh-Gordon model

Ayesha Naseem; Rashida Hussain; Ayesha Naseem; Rashida Hussain

doi:10.3934/math.2025793

AIMS Mathematics

2025, Volume 10, Issue 8: 17779-17800. doi: 10.3934/math.2025793

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Investigating novel soliton solutions and chaotic Structures for the (3+1)-dimensional fractional q-deformed tanh-Gordon model

Ayesha Naseem ,
Rashida Hussain ^,

Department of Mathematics, Mirpur University of Science and Technology, Mirpur-10250 (AJK), Pakistan

Received: 17 January 2025 Revised: 18 May 2025 Accepted: 20 May 2025 Published: 06 August 2025
MSC : 35Q51, 35C08, 37D45, 37G25

The generalized (3+1)-dimensional fractional q-deformed tanh-Gordon model and its optical solutions are studied under various physical conditions. Verifying our analytical findings and using the modified Sardar-sub equation technique (SSET) to examine the behavior of the governing model through convergence criteria under different parameters of the hyperbolic local derivative. By generating diverse optical phenomena and flexibility of the governing model, our findings pave the way for additional theoretical and applied physics research. The objective is also to study the bifurcation and chaotic behavior of the equation. To accomplish this, a dynamical system is created using the Galilean transformation. Analyzing the bifurcation and chaotic structure of the equation to identify important transitions that lead to chaotic behavior, and using phase-space analysis to understand the system's unpredictability. The study shows how small adjustments can have a significant effect on the results. This study clarifies the behavior of the model, which is crucial for several applications in quantum mechanics, physics, and optics.
- (3+1)-dimensional fractional q-deformed equation,
- hyperbolic local derivative,
- soliton solutions,
- SSET,
- bifurcation analysis,
- quasi-periodic chaotic structure,
- symbolic computation
Citation: Ayesha Naseem, Rashida Hussain. Investigating novel soliton solutions and chaotic Structures for the (3+1)-dimensional fractional q-deformed tanh-Gordon model[J]. AIMS Mathematics, 2025, 10(8): 17779-17800. doi: 10.3934/math.2025793

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Abstract

The generalized (3+1)-dimensional fractional q-deformed tanh-Gordon model and its optical solutions are studied under various physical conditions. Verifying our analytical findings and using the modified Sardar-sub equation technique (SSET) to examine the behavior of the governing model through convergence criteria under different parameters of the hyperbolic local derivative. By generating diverse optical phenomena and flexibility of the governing model, our findings pave the way for additional theoretical and applied physics research. The objective is also to study the bifurcation and chaotic behavior of the equation. To accomplish this, a dynamical system is created using the Galilean transformation. Analyzing the bifurcation and chaotic structure of the equation to identify important transitions that lead to chaotic behavior, and using phase-space analysis to understand the system's unpredictability. The study shows how small adjustments can have a significant effect on the results. This study clarifies the behavior of the model, which is crucial for several applications in quantum mechanics, physics, and optics.

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