A Regularization-Free Scheme for Recovering Large External Forces of Higher-Order Nonlinear Evolution Equations

Abstract

In this study, the inverse engineering problems of the Ostrovsky equation (OE), Kawahara equation (KE), modified Kawahara equation (mKE), and sixth-order Korteweg-de Vries (KdV) equation will be investigated numerically. An effective numerical approach to tackle these inverse Coriolis dispersion problems and the above-mentioned inverse problems are still not available. To use different boundary shape functions, we must deal with the boundary data, initial conditions, and terminal time conditions of the OE, KE, mKE, and sixth-order KdV equations. The unknown Coriolis dispersion of OE and unknown large external forces of those three equations can be retrieved through back-substitution of the solution into the OE, KE, mKE, and sixth-order KdV equations while we obtain the solution with the symmetry property by employing the boundary shape function scheme (BSFS). Five numerical experiments with noisy data are carefully validated and discussed.

Keywords

• Ostrovsky equation (OE)
• Kawahara equation (KE)
• modified Kawahara equation (mKE)
• sixth-order Korteweg-de Vries (KdV) equation
• boundary shape functions scheme (BSFS)
• inverse Coriolis dispersion problems