Analyzing the Impact of Nonlinear Wave Resonance on UAV Sea Surface Detection via a (2+1)-Dimensional Nonlinear Wave Equation

Sea surface detection capability of the unmanned aerial vehicles (UAVs) is widely discussed. However, the uncertainty and interaction of nonlinear ocean waves have brought challenges to the detection capabilities of the UAVs. This paper presents an analytic study on a (2+1)-dimensional nonlinear wave equation with the real variable coefficients, aiming to furnish theoretical underpinnings for improving the sea surface detection capabilities of UAVs. By leveraging the Pfaffian technique, Pfaffian solutions and N-soliton solutions with a time dependent real function for the equation are derived from the bilinear form we constructed. Asymptotic analysis is applied on the reduced three-soliton solutions, which reflect the mechanisms of resonant interaction between one solitary wave and one breather wave. Through the Pfaffian solutions, resonant interactions among the solitary waves and breather waves are discussed graphically. It is concluded that the real coefficients of the equation influence the characteristic lines and the time dependent real function influences the background plane of the nonlinear waves. Amplitudes of the waves are found to depend on the wave numbers. Analysis in this paper provides insights into the underlying phenomena, that could potentially improve the cooperative perception and sea surface detection capabilities of UAVs for future applications.