Traveling wave solutions to beam equation with fast-increasing nonlinear restoring forces (Q1576314)

The paper deals with traveling wave solutions of the beam equation \[ u_{tt}+ u_{xxxx}+ f(u)= 0, \] when the restoring force function is of the form: \(f(u)= u\cdot h(u)- 1\). The author proves that a traveling wave solution exists when \(h(u)\geq 1\) for \(u\geq 1\). The solution can be obtained as a saddle point in a variational formulation.