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<p>We derive analytical mean-field travelling wave solutions for the two-dimensional stochastic Nagumo and stochastic Burgers–Fisher equations using the Riccati–Bernoulli sub-ODE method. These equations, driven by multiplicative noise, play a crucial role in a wide range of natural applications. By applying a stochastic travelling wave transformation and the Riccati–Bernoulli equation, we convert each model into a system of algebraic equations, which restricts the solutions for travelling wave profiles. To validate the obtained mean-field solutions, strong numerical simulations of the studied SPDEs are presented, and the spatial rates of strong convergence in terms of mean of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> errors are calculated, showing that these solutions are indeed reliable. This study also explores how multiplicative noise affects travelling wave dynamics, with a particular focus on wave propagation failure at high noise levels. Additionally, we examine how noise intensity influences propagation speed, shedding light on the intricate interplay between stochastic effects and wave behaviour.</p>

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Mean-field travelling wave solutions using Riccati–Bernoulli sub-ODE method for two-dimensional stochastic Nagumo and stochastic Burgers–Fisher equations with applications in waves propagation failure

  • 期刊论文

  • 发表日期：

    2026年3月25日

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  • Hasan Alzubaidi

摘要

We derive analytical mean-field travelling wave solutions for the two-dimensional stochastic Nagumo and stochastic Burgers–Fisher equations using the Riccati–Bernoulli sub-ODE method. These equations, driven by multiplicative noise, play a crucial role in a wide range of natural applications. By applying a stochastic travelling wave transformation and the Riccati–Bernoulli equation, we convert each model into a system of algebraic equations, which restricts the solutions for travelling wave profiles. To validate the obtained mean-field solutions, strong numerical simulations of the studied SPDEs are presented, and the spatial rates of strong convergence in terms of mean of \(L_2\) L 2 errors are calculated, showing that these solutions are indeed reliable. This study also explores how multiplicative noise affects travelling wave dynamics, with a particular focus on wave propagation failure at high noise levels. Additionally, we examine how noise intensity influences propagation speed, shedding light on the intricate interplay between stochastic effects and wave behaviour.