Nonlinear wave dynamics and stable coherent structures in the complex Rangwala–Rao equation

This study investigates the nonlinear wave dynamics governed by the complex Rangwala–Rao (RR) equation, a prominent nonlinear evolution model describing dispersive–dissipative structures in physical, engineering and plasma environments. By employing the Khater II method, a spectrum of new exact solitary-wave solutions is constructed, including bright-type, singular, periodic and complex-modulated wave structures. The obtained solutions reveal rich dynamical behaviors that reflect the intrinsic balance between nonlinearity, dispersion and complex-valued interactions within the RR framework. In addition, the stability of the derived solutions is examined through a Hamiltonian-based formulation, where the phase-space properties, perturbation responses and energy variations provide clear criteria distinguishing stable coherent structures from unstable regimes. The combined analytical and dynamical treatment presented here enriches the theoretical understanding of nonlinear RR-type systems and highlights how solution morphology is shaped by parameter sensitivity, initial-energy configurations and the complex-valued nature of the model.