A Collision-State Criterion for Two-Peak Collisions in a Two-Dimensional Long-Wave–Short-Wave Resonance Interaction System

This Letter investigates the finite-time morphology of two-pulse collisions in a two-dimensional long-wave-short-wave resonance interaction system with a local cubic perturbation. An integral identity for the centered second moment separates the collision dynamics into contributions from dispersive spreading, local quartic overlap, and long-wave feedback. For the prescribed two-sech initial-data family and the finite observation interval T ≤ 7, these contributions distinguish double-peak (DP) and single-peak (SP) morphologies with an accuracy of 94.17%. A feedforward neural network is then employed to efficiently reconstruct the distribution of the identity-based result in the parameter plane of the nonintegrable coefficient and relative phase. This distribution shows that variation of the relative phase can change the collision morphology.