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June 10, 2026MathematicsOpen Access

Exact Nonlinear Wave Solutions and Interaction Dynamics of the Integrable Kairat-II-X Equation via Improved Riccati Neural Networks

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Authors

GTGhulam Hussain TipuKhazar UniversityFYFengping YaoShanghai UniversityAMAbdul MateenShandong Normal University

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Overview

Randomized trial explores nonlinear wave dynamics in higher-dimensional systems, highlighting analytical techniques for wave solutions.

Key Points

  • This study aims to investigate the nonlinear wave dynamics of the Kairat-II-X equation and derive its exact solutions.
  • Implemented an improved Riccati neural networks (IRNNs) framework to derive analytical solutions.
  • Constructed trial functions using multilayer neural network structures for the K-II-X equation.
  • Illustrated wave structures through various visualizations to analyze wave behavior and interaction.
  • Derived several classes of exact wave solutions including hyperbolic, trigonometric, and rational forms.
  • Produced single- and multisoliton wave profiles demonstrating nonlinear localization and interaction behavior.
  • Visualizations revealed the influence of governing parameters on wave amplitude and propagation.

Cite This Study

Tipu et al. (2026) studied this question.

synapsesocial.com/papers/6a28fff36f82f25be989cb14https://doi.org/10.3390/math14122048
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