 EqWorld The World of Mathematical Equations Exact Solutions > Nonlinear Partial Differential Equations > Second-Order Hyperbolic Partial Differential Equations ## 2. Nonlinear Hyperbolic Equations

### 2.1. Nonlinear Wave Equations of the Form wtt = awxx + f(w)

1. wtt = awxx + aw + bwn.    Klein--Gordon equation with a power-law nonlinearity.
2. wtt = wxx + awn + bw2n−1.    Klein--Gordon equation with a power-law nonlinearity.
3. wtt = a2wxx + beβw.    Modified Liouville equation.
4. wtt = wxx + aeβw + bew.    Klein--Gordon equation with a exponential nonlinearity.
5. wtt = awxx + b sinh(λw).    Sinh--Gordon equation.
6. wtt = awxx + b sin(λw).    Sine--Gordon equation.
7. wtt = wxx + f(w).    Nonlinear Klein--Gordon equation.

### 2.2. Other Nonlinear Hyperbolic Equations

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