Modulational instability and impact of potassium leakage on Nerve Pulse Propagation in a Weakly Dissipative Myelinated Axon

Modulational instability and impact of potassium leakage on Nerve Pulse Propagation in a Weakly Dissipative Myelinated Axon | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Modulational instability and impact of potassium leakage on Nerve Pulse Propagation in a Weakly Dissipative Myelinated Axon Arnaud Djine, Serge Bruno Yamgoue This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9663653/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract In this paper, we investigate the impact of ionic leakage currents and perform a modulational instability analysis in a weakly dissipative myelinated axon. Using the well-known FitzHugh–Nagumo equation, we derive a generalized discrete nonlinear lattice equation, from which the dispersion relation and group velocity are obtained, allowing us to examine the influence of leakage. Applying the reductive perturbation method, we derive a cubic complex Schr"odinger equation, followed by a modulational instability analysis. An ansatz is introduced to obtain exact solutions, and by direct integration, solitary wave solutions are explicitly obtained, including bright and dark solitons, as well as a periodic solution. The effect of potassium ion leakage is clearly reflected in these solutions, significantly affecting the amplitude of the solitons. Finally, numerical simulations using the finite difference method are performed, showing excellent agreement with the analytical results. Potassium leakage FitzHugh-Nagumo Model Reductive perturbation Solitary waves Full Text Additional Declarations No competing interests reported. Supplementary Files INtrodUctiona.pdf Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 12 May, 2026 Editor assigned by journal 11 May, 2026 Submission checks completed at journal 11 May, 2026 First submitted to journal 09 May, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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