Nonlinear oscillator with discontinuity by parameter-expansion method

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Periodic Solution for Strongly Nonlinear Vibration Systems by He’s Energy Balance Method (2009, methodology): “To overcome the shortcomings, many new techniques have appeared in open literature [3–14], such as non-perturbative methods [3], homotopy perturbation method [4–7], perturbation techniques [8], Lindstedt–Poincare method [9, 10], parameter–expansion method [ 11 , 12] and parameterized perturbation me”
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review (2012, unknown): “PEM was successfully applied to 500 various engineering problems [8, 42, 69, 97, 103, 118, 134, 147, 161, 190, 195–197, 201].”
Modified Kudryashov method for finding exact solitary wave solutions of higher‐order nonlinear equations (2011, methodology): “The variational iteration method [1--6], the homotopy perturbation method [7--10], the tanh-method [11, 12], the extended tanh-method [13], the parameter-expansion method [14, 15], the homogeneous balance method [16, 17], the inverse scattering method [18, 19], Exp-function method [20--25] are some ”