it is noticed that the nonlinear models have been used in applications where vibrations isolation systems are needed such as suspension systems in vehicles , separation of machines from the floor , buildings and bridges so that optimum reduction in the transfer of vibration from / to structures is obtained and at the same high bearing capacity is maintained
Solitary Wave equations, which are nonlinear are known as the exact solvable systems of equations in practice: Such as: Korteweg-de Vries, Sin-Gondon, Einstein's field equation.
As a matter of fact non-linear problems which admit generalized separation of variables form, are having closed form solutions.
One must distinguish between problems which have some closed form solutions (this may only require some amount of symmetry), and systems which are integrable (i.e., that all solutions --- in some sense --- have a closed form). The Einstein equations of gravity is an example of the first type. The Korteweg-de Vries and Sine-Gordon equations in two space-time dimensions are examples of the second type.
It is scientifically more profitable to search for symmetric solutions of an interesting problem than integrability of uninteresting problem.
According to my life long experience - forget about to look for a closed form but it is nonsense to expect to find analytic solutions for the nonlinear mechanical systems having complicated constrains such as nonholonomic -inequality- and/or rheonomous -time dependent- versions. Therefore try to solve the problem if you can by various numerical integration techniques suitable for your special problem. Mostly you have to design your own method by using your own experience and intuition. BEST REGARDS
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