Exact Solutions > Nonlinear Partial Differential Equations > Third-Order Partial Differential Equations

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5. Third-Order Partial Differential Equations

1. w_t + w_xxx − 6ww_x = 0.    Korteweg--de Vries equation.
2. w_t + w_xxx − 6ww_x + (2t)⁻¹w = 0.    Cylindrical Korteweg--de Vries equation.
3. w_t + w_xxx + 6σw²w_x = 0.    Modified Korteweg--de Vries equation.
4. w_t + w_xxx + f(w)w_x = 0.    Generalized Korteweg--de Vries equation.
5. w_yw_xy − w_xw_yy = aw_yyy.    Hydrodynamic boundary layer equation.
6. w_yw_xy − w_xw_yy = aw_yyy + f(x).    Boundary layer equation with pressure gradient.