New solitary wave solitons, analysis and simulations of the FitzHugh–Nagumo Model

Devraj Maurya, Ajeet Singh and Ram Jiwari

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 384-403

Abstract: In this work, we construct new solitons of the FitzHugh–Nagumo model using the tanh–coth and Kudryashov methods. After that we analyze and simulate the model by developing a finite element method with BDF1 scheme. For existence and uniqueness of weak solutions, we use the fixed point theorem and a Lyapunov functional to derive a priori bounds. Optimal error estimates in H1 and L2 norms are derived for the FEM-BDF1 scheme and the nonlinearity is handled using the mean value theorem. In the numerical tests, we demonstrate the theoretical convergence rates and also capture the spiral wave behavior of the solution.

Keywords: Solitons; Finite element method; Lyapunov functional; Error estimates; Stability analysis; BDF1 scheme (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:384-403

DOI: 10.1016/j.matcom.2026.04.027

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