Compacton
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In the theory of integrable systems, a compacton (introduced in ) is a soliton with compact support. An example of an equation with compacton solutions is the generalization : u_t+(u^m)_x+(u^n)_{xxx}=0\, of the Korteweg–de Vries equation (KdV equation) with m, n > 1. The case with m = n is the Rosenau–Hyman equation as used in their 1993 study; the case m = 2, n = 1 is essentially the KdV equation.
In the theory of integrable systems, a compacton (introduced in ) is a soliton with compact support. An example of an equation with compacton solutions is the generalization u_t+(u^m)_x+(u^n)_{xxx}=0\, of the Korteweg–de Vries equation (KdV equation) with m, n > 1. The case with m = n is the Rosenau–Hyman equation as used in their 1993 study; the case m = 2, n = 1 is essentially the KdV equation. ==Example== The equation u_t+(u^2)_x+(u^2)_{xxx}=0 \, has a travelling wave solution given by u(x,t) = \begin{cases} \dfrac{4\lambda}{3}\cos^2((x-\lambda t)/4) & \text{if }|x - \lambda t| \le 2\pi, \\ \\ 0 & \text{if }|x - \lambda t| \ge 2\pi. \end{cases} This has compact support in x, and so is a compacton. ==See also== Peakon Vector soliton ==References==
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