Exact Solutions > Linear Partial Differential Equations > Second-Order Hyperbolic Partial Differential Equations

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2. Linear Hyperbolic Equations

1. w_tt = a²w_xx.    Wave equation (linear wave equation).
2. w_tt = a²w_xx + Φ(x, t).    Nonhomogeneous wave equation.
3. w_tt = a²w_xx − bw.    Klein-Gordon equation.
4. w_tt = a²w_xx − bw + Φ(x, t).    Nonhomogeneous Klein-Gordon equation.
5. w_tt = a²(w_rr + r⁻¹w_r) + Φ(r, t).    Nonhomogeneous wave equation with axial symmetry.
6. w_tt = a²(w_rr+2r⁻¹w_r) + Φ(r, t).    Nonhomogeneous wave equation with central symmetry.
7. w_tt + kw_t = a²w_xx + bw.    Telegraph equation.