Exact Solutions > Nonlinear Partial Differential Equations > Other Second-Order Partial Differential Equations

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4. Other Second-Order Partial Differential Equations

4.1. Equations of Transonic Gas Flow

1. aw_xw_xx + w_yy = 0.    Equation of steady transonic gas flow.
2. w_yy + ay⁻¹w_y + bw_xw_xx = 0.    Equation of steady transonic gas flow.

4.2. Monge-Ampere Equations

1. (w_xy)² − w_xxw_yy = 0.    Homogeneous Monge-Ampere equation.
2. (w_xy)² − w_xxw_yy = A.    Nonhomogeneous Monge-Ampere equation.
3. (w_xy)² − w_xxw_yy = F(x, y).    Nonhomogeneous Monge-Ampere equation.