Novel Numerical Approach to Solitary–wave Solutions Identification of Boussinesq and Korteweg–de Vries Equations

A special numerical technique has been developed for identification of solitary wave solutions of Boussinesq and Korteweg–de Vries equations. Stationary localized waves are considered in the frame moving to the right. The original ill-posed problem is transferred into a problem of the unknown coefficient from over-posed boundary data in which the trivial solution is excluded. The Method of Variational Imbedding is used for solving the inverse problem. The generalized sixth-order Boussinesq equation is considered for illustrations.