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arXiv · 2601.16854

Stochastic Analysis of Fifth-Order KdV Soliton in Damping Regime and Reduction to Painlev\'e Second Equation

Irfan Mahmood·Adeena Iqbal·Sohail Mumtaz
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Abstract

This work presents a stochastic analysis of fifth-order KdV soliton momentum distribution in a damping regime. An explicit representation of the soliton momentum associated with amplitude variation is derived in terms of a random time function in the presence of dissipation. Statistical interpretations of soliton propagation modes, amplitude fluctuations, and amplification are analyzed within a $\delta$-correlated Gaussian random framework. Graphical results obtained using Python illustrate the physical insight into amplitude fluctuation and energy flow. Finally, under a dominant approximation, the nonlinear momentum evolution equation is shown to reduce to the Painlev\'e second equation, a well-known integrable model appearing in diverse physical systems.

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Irfan Mahmood, Adeena Iqbal, Sohail Mumtaz. 2026-01-23. Stochastic Analysis of Fifth-Order KdV Soliton in Damping Regime and Reduction to Painlev\'e Second Equation. https://arxiv.org/abs/2601.16854

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