Purpose

In the nonlinear model of reaction–diffusion, the Fitzhugh–Nagumo equation plays a very significant role. This paper aims to generate innovative solitary solutions of the Fitzhugh–Nagumo equation through the use of variational formulation.

Design/methodology/approach

The partial differential equation of Fitzhugh–Nagumo is modified by the appropriate wave transforms into a dimensionless nonlinear ordinary differential equation, which is solved by a semi-inverse variational method.

Findings

This paper uses a variational approach to the Fitzhugh–Nagumo equation developing new solitary solutions. The condition for the continuation of new solitary solutions has been met. In addition, this paper sets out the Fitzhugh–Nagumo equation fractal model and its variational principle. The findings of the solitary solutions have shown that the suggested method is very reliable and efficient. The suggested algorithm is very effective and is almost ideal for use in such problems.

Originality/value

The Fitzhugh–Nagumo equation is an important nonlinear equation for reaction–diffusion and is typically used for modeling nerve impulses transmission. The Fitzhugh–Nagumo equation is reduced to the real Newell–Whitehead equation if β = −1. This study provides researchers with an extremely useful source of information in this area.

中文翻译：

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非线性反应扩散方程中FitzHugh-Nagumo方程新孤子解的变分方法

目的

在反应扩散的非线性模型中，Fitzhugh-Nagumo方程起着非常重要的作用。本文旨在通过使用变分公式来产生Fitzhugh–Nagumo方程的创新孤立解。

设计/方法/方法

通过适当的波变换将Fitzhugh–Nagumo的偏微分方程修改为无量纲的非线性常微分方程，并通过半逆变分法对其进行求解。

发现

本文对Fitzhugh-Nagumo方程采用变分方法来开发新的孤立解。满足了新的单独解决方案的条件已得到满足。此外，本文提出了Fitzhugh-Nagumo方程的分形模型及其变分原理。单独解决方案的发现表明，所提出的方法是非常可靠和有效的。建议的算法非常有效，几乎是解决此类问题的理想选择。

创意/价值

Fitzhugh–Nagumo方程是反应扩散的重要非线性方程，通常用于模拟神经冲动的传递。如果β= -1，则Fitzhugh–Nagumo方程简化为真实的Newell–Whitehead方程。这项研究为研究人员在这一领域提供了极为有用的信息资源。