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Persistence properties and unique continuation of solutions of the Camassa-Holm equation. (English) Zbl 1142.35078

The authors study the Camassa-Holm equation

u t -u txx +3uu x -2u x u xx -uu xxx =0,

which physically was derived as a shallow water equation admitting peaked solitons. They prove that, given a strong solution to the Cauchy problem for this equation such that the initial data u(x,0) decays exponentially together with the spatial derivative, if at some time t 1 >0 the solution u(x,t 1 ) decays exponentially in x then u is identically zero: u(x,t)0.

35Q53KdV-like (Korteweg-de Vries) equations
35Q35PDEs in connection with fluid mechanics
35B60Continuation of solutions of PDE
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