Two Distinct Group Reductions Leading to Integrable Coupled mKdV Models

Key Points

• The aim is to investigate distinct group reductions of the Ablowitz–Kaup–Newell–Segur matrix problem to develop integrable coupled mKdV models.
• Formulated three distinct group reduction schemes.
• Derived new integrable coupled mKdV systems from these reductions.
• Analyzed the implications for the classification of third-order integrable equations.
• Introduced novel examples of integrable coupled mKdV systems.
• Provided fresh insights into the classification strategy for third-order integrable equations.