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August 27, 2026International Journal of Bifurcation and Chaos

Analyzing Bifurcation Phenomena, Quasiperiodic Patterns, and Wave Structures of the Time-Fractional Benjamin–Bona–Mahony–Burger Equation

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Authors

SKSourav KumawatSKSandeep KaurBBBharat Bhushan

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Overview

Mathematical modeling reveals soliton solutions, bifurcation phenomena, and chaotic trajectories in time-fractional BBM-Burger systems, highlighting nonlinear wave mechanisms in dispersive media.

Key Points

  • Investigate exact soliton solutions, bifurcation behaviors, and chaotic dynamics within the time-fractional Benjamin–Bona–Mahony–Burger equation representing unidirectional long waves.
  • Applied an algebraic expansion method to derive analytical soliton solutions categorized into hyperbolic, trigonometric, and rational families.
  • Constructed 3D visual representations across four fractional-order values to evaluate the influence of the fractional variable on wave structures.
  • Reduced the governing equation into a planar dynamical system to evaluate phase portraits, fixed points, Lyapunov exponents, and Poincaré sections.
  • Derived parameterized soliton solutions showing structural transitions governed by variations in the fractional derivative parameter.
  • Identified equilibrium points and determined the parameter conditions that trigger bifurcation and the onset of chaotic wave trajectories.

Cite This Study

Kumawat et al. (2026) studied this question.

synapsesocial.com/papers/6a8fea0d10c91c1e926220aahttps://doi.org/10.1142/s0218127426502068
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