Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation
نویسندگان
چکیده
In this paper, we study numerically the existence and stability of some special solutions of the nonlinear beam equation: utt +uxxxx +u− |u|p−1u = 0 when p = 3 and p = 5. First we show the existence and the orbital stability of the standing wave solutions: u(x, t) = eφω(x). Next, we study the existence and linear stability of the traveling wave solutions: u(x, t) = φ(x + ct). For both types of solutions, we present the numerical results for the bounds for ω and c that divide the intervals of stability and the intervals of instability.
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