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The system of partial differential equations del ^2s-(|a|^2+1)s = 0 (1) del ^2a-del (del ·a)-s^2a = a. (2)

The partial differential equation u_t=u_(xxxxx)+5/2u_(xxx)u+(25)/4u_(xx)u_x+5/4u^2u_x.

The system of partial differential equations u_t+uu_x+vu_y=U_t+UU_x+mu/rhou_(yy) u_x+v_y=0.

A relation "<=" is called a preorder (or quasiorder) on a set S if it satisfies: 1. Reflexivity: a<=a for all a in S. 2. Transitivity: a<=b and b<=c implies a<=c. A preorder ...

The system of partial differential equations E_t-v = 0 (1) r_x+omegav = 0 (2) q_x+Ev = 0 (3) v_x-omegar-Eq = 0. (4)

The method for solving the Goursat problem and Cauchy problem for linear hyperbolic partial differential equations using a Riemann function.

The partial differential equation u_t+45u^2u_x+15u_xu_(xx)+15uu_(xxx)+u_(xxxxx)=0.

The partial differential equation del ^2A=-del xE, where del ^2 is the vector Laplacian.

If a minimal surface is given by the equation z=f(x,y) and f has continuous first and second partial derivatives for all real x and y, then f is a plane.

The so-called generalized Kadomtsev-Petviashvili-Burgers equation is the partial differential equation ...