In particular, \(u_{1,2}\) may represent solitary waves, that is, the waves with a finite support or decaying exponentially at infinity. However, it can happen that such a wave equation is only a zero approximation, that is not enough even for a qualitative description of the phenomenon. A simplest adequate equation, having the linear equation as the limit, usually have to contain higher-order derivatives and nonlinearity. There exist such developed wave equations, which, in particular, define solitary waves propagating with a permanent form. Unlike the linear ones a nonlinear solitary wave have a specific form, defined by the corresponding nonlinear equation, and the wave speed does depend on the wave amplitude, i.e., on the wave energy. The above-considered 3D waves in a string (Sect.  10.7 ) represent an example of the nonlinear solitary waves.