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<p>This article aims to investigate approximate solutions for a class of stochastic partial differential equations with quadratic nonlinearities, perturbed by both additive and multiplicative noise. Our approach is based on amplitude equations, which capture the essential dynamics of the dominant modes. We derive approximate solutions using these amplitude equations and rigorously prove that they provide a good approximation to the original solutions. Moreover, our results reveal that noise has the potential to shift the bifurcation point.</p>

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Amplitude equations for SPDEs with quadratic nonlinearities by additive and multiplicative noise

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Shiduo Qu,
  • Wenlei Li,
  • Shaoyun Shi

摘要

This article aims to investigate approximate solutions for a class of stochastic partial differential equations with quadratic nonlinearities, perturbed by both additive and multiplicative noise. Our approach is based on amplitude equations, which capture the essential dynamics of the dominant modes. We derive approximate solutions using these amplitude equations and rigorously prove that they provide a good approximation to the original solutions. Moreover, our results reveal that noise has the potential to shift the bifurcation point.