LUMP, BREATHER, AND CHAOTIC DYNAMICS OF THE VARIABLECOEFFICIENT EXTENDED BLMP EQUATION

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Isah M. A., Muhammad A.

The 2nd International Conference on Modern Problems of Mathematics, Mechanics and Their Applications (MPMMA 2026), Baku, Azerbaycan, 23 - 25 Haziran 2026, ss.83-84, (Özet Bildiri)

Özet

In this work, we investigate the extended Boiti-Leon-Manna-Pempinelli (eBLMP) equation with time-dependent coefficients from two complementary perspectives: integrable soliton solutions and chaotic dynamics. First, starting from the (3+1)-dimensional variable-coefficient BLMP equation, we perform a dimensional reduction to obtain a (2+1)-dimensional extended model. We extend the analysis by allowing the dispersion coefficient 𝛼(𝑡) and nonlinearity coefficient 𝛽(𝑡) to be functions of time. We demonstrate that bilinearization imposes a proportionality condition 𝛼(𝑡)𝛽(𝑡) is constant. Under this condition, we construct lump solutions, lump-soliton interaction solutions, and breather solutions using Hirota's bilinear method. Second, through a traveling wave reduction, we obtain a planar dynamical system. Under periodic perturbation, this system exhibits deterministic chaos, characterized by phase portraits, Poincar\'e maps, a positive Lyapunov exponent 𝜆≈0.12, and sensitivity to initial conditions. The influence of time-dependent coefficients on wave dynamics is analyzed, revealing novel propagation properties. All solutions are presented in explicit form with graphical representations. A critical assessment of the limitations and physical interpretation of the proportionality condition is provided.