Stochastic Analysis of Fifth-Order KdV Soliton in Damping Regime and Reduction to Painlevé Second Equation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909999100329984 |
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| author | Mahmood, Irfan Iqbal, Adeena Mumtaz, Sohail |
| author_facet | Mahmood, Irfan Iqbal, Adeena Mumtaz, Sohail |
| contents | 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 $δ$-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 Painlevé second equation, a well-known integrable model appearing in diverse physical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16854 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Analysis of Fifth-Order KdV Soliton in Damping Regime and Reduction to Painlevé Second Equation Mahmood, Irfan Iqbal, Adeena Mumtaz, Sohail Mathematical Physics 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 $δ$-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 Painlevé second equation, a well-known integrable model appearing in diverse physical systems. |
| title | Stochastic Analysis of Fifth-Order KdV Soliton in Damping Regime and Reduction to Painlevé Second Equation |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2601.16854 |