1.2. EXAMPLES 5 b. Nonlinear equations. 1. Eikonal equation |Du| = 1. 2. Nonlinear Poisson equation −Δu = f(u). 3. p-Laplacian equation div(|Du|p−2Du) = 0. 4. Minimal surface equation div Du (1 + |Du|2)1/2 = 0. 5. Monge–Amp` ere equation det(D2u) = f. 6. Hamilton–Jacobi equation ut + H(Du, x) = 0. 7. Scalar conservation law ut + div F(u) = 0. 8. Inviscid Burgers’ equation ut + uux = 0. 9. Scalar reaction-diffusion equation ut − Δu = f(u). 10. Porous medium equation ut − Δ(uγ) = 0. 11. Nonlinear wave equation utt − Δu + f(u) = 0. 12. Korteweg–deVries (KdV) equation ut + uux + uxxx = 0. 13. Nonlinear Schr¨ odinger equation iut + Δu = f(|u|2)u.

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