Nonisospectral water wave field: Fast and adaptive modal identification and prediction via reduced-order nonlinear solutions

Real-world water wave fields exhibit significant nonlinear and nonisospectral characteristics, making it challenging to predict their evolution by relying solely on numerical simulation or exact solutions using integrable system theory. Hence, this paper introduces a fast and adaptive method of modal identification and prediction in nonisospectral water wave fields using the reduced-order nonlinear solution (RONS) scheme. Specifically, we discuss the coarse graining and mode extraction of wave field snapshots from the data-driven and physics-driven perspectives and utilize the RONS method for principle modal prediction of nonisospectral water wave fields. This is achieved by investigating the standard and nonisospectral Gardner system describing nonlinear water waves as a demonstration. Through detailed comparison and analysis, the fundamental solitary behaviors and dispersive effects in the Gardner system are discussed. Subsequently, a neighbor approximation is developed that combines the essences of symbolic precomputation and numerical computation in the RONS procedure, which exploits the locality of nonlinear interactions in water wave fields.