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Exact solution of a quadratic nonlinear oscillator. (English) Zbl 1243.34001
Summary: The exact solution of a quadratic nonlinear oscillator (QNO) is presented by using the Jacobian elliptic sine function. The constants in the solution are expressed in terms of the initial conditions. The formulas for the period of oscillation \(T\) and amplitude \(B\) (for \(x\leq 0\)) are also given. This exact solution can serve as a benchmark solution for various approximate solutions. It also can be utilized for educational purpose.

MSC:
34A05 Explicit solutions, first integrals of ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K99 Nonlinear dynamics in mechanics
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