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The partial differential equation (1-u_t^2)u_(xx)+2u_xu_tu_(xt)-(1+u_x^2)u_(tt)=0.

An extension of the secant method of root finding to higher dimensions.

The partial differential equation u_t=del ·[M(u)del ((partialf)/(partialu)-Kdel ^2u)].

The system of partial differential equations u_t+u_x = v^2-u^2 (1) v_t-v_x = u^2-v^2. (2)

The partial differential equation R[u](u_(rr)+(u_r)/r+u_(zz))=u_r^2+u_z^2, where R[u] is the real part of u (Calogero and Degasperis 1982, p. 62; Zwillinger 1997, p. 131).

The partial differential equation u_(xy)+(N(u_x+u_y))/(x+y)=0.

Let f:R×R->R be a one-parameter family of C^3 maps satisfying f(0,0) = 0 (1) [(partialf)/(partialx)]_(mu=0,x=0) = -1 (2) [(partial^2f)/(partialx^2)]_(mu=0,x=0) < 0 (3) ...

The partial differential equation w_t-6(w+epsilon^2w^2)w_x+w_(xxx)=0, which can also be rewritten (w)_t+(-3w^2-2epsilon^2w^3+w_(xx))_x=0.

A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...

The partial differential equation u_t=u_(xxx)u^3.