The homotopy perturbation method (HPM) was proposed by Ji-Huan. He was a rising star in
analytical methods, and all traditional analytical methods had abdicated their crowns. It is …

The fractal Toda oscillator with an exponentially nonlinear term is extremely difficult to solve;
Elias-Zuniga et al.(2020) suggested the equivalent power-form method. In this paper, first …

The current study examines the hybrid Rayleigh–Van der Pol–Duffing oscillator (HRVD) with
a cubic–quintic nonlinear term and an external excited force. The Poincaré–Lindstedt …

The Hamiltonian-based frequency formulation has been hailed as an unprecedented
success for it gives a straightforward insight into a complex nonlinear vibration system with …

A concrete beam is a basic element for many applications in architectural engineering, and
its vibration property plays an important role in safety and life-span. Previous vibration …

A variational formulation is extremely difficult to be established for a strongly nonlinear
problem, and it is almost impossible for a singular differential equation without linear terms …

A modification of the homotopy perturbation method is suggested with three effective
expansions to solve a nonlinear oscillator with damping terms to expand the solution, the …

In this paper, we aim to study the (1+ 2)-dimensional chiral nonlinear Schrödinger equation.
A complex transform is adopted to convert the equation into the real and imaginary parts …

The comprehensive formularization of the frequency–amplitude formula is the main interest
in this work to cover higher powers of the restoring force which are not limited to cubic …

The frequency-amplitude relationship is pivotal in understanding oscillatory systems,
dictating their dynamic behaviors and responses. This paper delves into the intricacies of the …