A nonlinear scattering length formula in the p-Laplacian framework

Xinyu Hu

Chaos, Solitons & Fractals, 2025, vol. 192, issue C

Abstract: This paper investigates nonlinear diffusion processes within the framework of the p-Laplacian operator, focusing on the interplay between path integrals, cumulative potential, and scattering length. We propose a novel nonlinear scattering length definition, suitable for multi-scale, multi-state systems with non-uniform diffusion. Furthermore, we derive analytical results that reveal connections between the first eigenvalue, energy functionals, and scattering properties, offering new insights into statistical models and nonlinear dynamics. To better capture the dynamics governed by the p-Laplacian operator, we employ nonlinearity-driven stochastic processes as a conceptual framework instead of relying on Brownian-like motion models.

Keywords: p-Laplacian; Nonlinear scattering length; Cumulative potential; Statistical computing; Path integral (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077924015108

DOI: 10.1016/j.chaos.2024.115958

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