A remark on the korteweg-de vries equation
Copyright policy ) CALOGERO, Francesco;
A remark on the korteweg-de vries equation
Let u(x, t) be a solution of the KdV equation ut — uxxx— 6uxu = 0, z(x,t) be a solution of the first-order PDE zt- 2uzx = 0 and v(z) be defined in terms of u and z by the formula r[z(x,i),t] = [zx(x,t)]-2 u(x,t) — [zx(x,t)]-1/2[zx{x,t)-1/2}xx. Then vt(z,t) = 0, namely v(z,t) does not change with time (for fixed z).
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