Physics-informed neural networks with energy constraints for coupled KdV equations: analytical and computational insights into soliton interactions

Key Points

• Interactions of solitons are accurately captured using physics-informed neural networks, enhancing model precision.
• The study highlights energy constraints resulting in more reliable analytical insights into KdV equations' behavior.
• Analysis employed physics-informed neural networks to evaluate soliton interactions in coupled KdV equations.
• Findings indicate that energy-constrained approaches may lead to significant advancements in computational techniques for nonlinear wave equations.