Reconstruction of coefficients of higher order nonlinear wave equations by measuring solitary waves

• Inverse problems for 5th and 6th order nonlinear wave equations are studied.
• The problems use measurements of characteristics of solitary waves.
• The uniqueness of solutions is shown and direct algorithms are deduced.

Inverse problems to recover coefficients of the fifth order KdV equation, sixth order generalized Boussinesq equation (SGBE) and two sixth order equations occurring in the dynamics of multiscale microstructure are considered. It is proposed to use characteristics of solitary waves for solving the inverse problems. The uniqueness of the solutions is shown and solution algorithms are provided. Several numerical examples are presented.