Exact Soliton, Breather and Hybrid Interaction Solutions for a Generalized Fifth-Order Korteweg-de Vries Equation

Abstract We study a generalized fifth-order KdV equation with quadratic/cubic nonlinearities and coupled third-fifth-order dispersion terms, capable of modeling strongly nonlinear waves in stratified shallow water, plasmas and optical fibers beyond the classical KdV regime. Using the Hirota bilinear method, we derive its exact bilinear equation under strict coefficient constraints and construct unified analytical N-soliton expressions with explicit 1-, 2- and 3-soliton examples. Complex conjugate wave pairs are adopted to generate single and double breathers with tunable spatiotemporal oscillation periods. Two novel families of soliton-breather hybrid interaction solutions are constructed, which have seldom been reported for high-order KdV-type models. Visualizations of the exact analytical solutions via 2D cross-sections, 3D evolution surfaces and density contours illustrate elastic collisions, periodic oscillations and intricate coupled wave dynamics. The analytical results provide rigorous theoretical foundations for subsequent research on high-order dispersive nonlinear evolution equations.