Solving nonlinear Hamiltonian amplitude equation: novel insights and computational strategies.

This research provides the first known solution to the nonlinear Hamiltonian amplitude equation using the combined Bernoulli sub-equation function and trigonometric-quintic-B-spline methods. While previous works have analyzed this model through limited linear approximations, an exact solution accounting for nonlinearity remains lacking. We address this gap by employing innovative techniques to reveal and scrutinize solitary wave solutions, elucidating complex behaviors inaccessible through linear methods. Our findings show the unequivocal effectiveness of our approach, comprising the first successful solution to this equation. This breakthrough fundamentally advances the comprehension of nonlinear physical systems across domains encompassing wave propagation, quantum mechanics, and optical phenomena. [ABSTRACT FROM AUTHOR]