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

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Title: New solitary wave solitons, analysis and simulations of the FitzHugh–Nagumo Model.
Authors: Maurya, Devraj1 (AUTHOR) devraj_m@ma.iitr.ac.in, Singh, Ajeet1 (AUTHOR) ajeet_s@ma.iitr.ac.in, Jiwari, Ram1 (AUTHOR) ram.jiwari@ma.iitr.ac.in
Source: Mathematics & Computers in Simulation. Oct2026, Vol. 248, p384-403. 20p.
Subjects: Solitons, Finite element method, Uniqueness (Mathematics), Computer simulation, Mathematical models, Lyapunov functions, Approximation error
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 H 1 and L 2 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. • New solitons of FHN model are obtained by the tanh–coth and Kudryashov methods. • The model is analyzed and simulated by a FEM with BDF1 scheme. • Existence and uniqueness of weak solutions as well as a priori bounds are derived. • Optimal error estimates in Ĥ1 and L̂2 norms are derived. • Numerical validation is done through the obtained solutions using FEM. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
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 H 1 and L 2 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. • New solitons of FHN model are obtained by the tanh–coth and Kudryashov methods. • The model is analyzed and simulated by a FEM with BDF1 scheme. • Existence and uniqueness of weak solutions as well as a priori bounds are derived. • Optimal error estimates in Ĥ1 and L̂2 norms are derived. • Numerical validation is done through the obtained solutions using FEM. [ABSTRACT FROM AUTHOR]
ISSN:03784754
DOI:10.1016/j.matcom.2026.04.027