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February 25, 2026Modern Physics Letters B

Exploring exact wave solutions of the Cahn–Allen equation via a novel Bernoulli sub-equation neural networks method

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Authors

KWKANG-JIA WANG

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Overview

This work explores exact wave solutions in the Cahn–Allen equation using a novel neural network approach, suggesting new mathematical links.

Key Points

  • To develop exact wave solutions of the Cahn–Allen equation using a novel Bernoulli sub-equation neural network method.
  • Proposed a new Bernoulli sub-equation neural network method.
  • Used Bernoulli sub-equation functions as activation functions in neural networks.
  • Constructed two different ‘2-2-2-1’ neural network models with distinct second layer activation functions.
  • Utilized trial functions to derive various exact wave solutions.
  • Successfully established new exact wave solutions for the Cahn–Allen equation.
  • Illustrated the wave shapes using Maple software.
  • Provided a methodology applicable to explore exact solutions of other non-linear partial differential equations.

Cite This Study

KANG-JIA WANG (2026) studied this question.

synapsesocial.com/papers/699e912ef5123be5ed04e88fhttps://doi.org/10.1142/s0217984926500624
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