Chaotic dynamics and soliton structures of the (3+1)-dimensional Hirota model with application to secure image encryption

This work explores complex dynamical analysis of a new (3+1)-dimensional Hirota model, which has not yet studied in the literature. The wave transformation approach is utilized and the proposed model is reduced into system of ordinary differential equations (ODEs), which is further examined through nonlinear analysis, including phase portraits and power spectra. By applying the new Kudryashov method (KM), both bright and dark solitary wave solutions are explicitly derived. Furthermore, novel application of chaotic characteristics of the proposed model in image encryption and decryption is presented. The numerical experimental validation confirms the effectiveness of the model in secure digital images transfer, achieving entropy values close to the ideal 8 (e.g., 7.999 for Lena), correlation coefficients near zero, high NPCR ( $>99.57\%$ ), and UACI in the range of 30–33%. These findings demonstrate the robustness of the encryption scheme against statistical and differential attacks. Overall, this study offers significant contributions to the theoretical analysis of solitons, chaos, and their practical applications in secure communications.