Auxiliary Solutions via Dimension Reduction for the (2+1)-Dimensional Calogero–Bogoyavlenskii–Schiff Equation Based on a Bilinear Neural Network Method Coupled with Symbolic Computation
Nonlinear partial differential equations formed the mathematical core of nonlinear science. They revealed the intrinsic link between algebraic structures and complex dynamical behaviors. Traditional analytical and numerical methods, however, faced high computational costs, cumbersome derivations, limited accuracy, and...