Abstract We classify generalized Camassa–Holm-type equations which possess infinite
hierarchies of higher symmetries. We show that the obtained equations can be treated as …

Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …

We present a new integrable partial differential equation found by Vladimir Novikov. Like the
Camassa–Holm and Degasperis–Procesi equations, this new equation admits peaked …

Nonlinear differential or difference equations are encountered not only in mathematics but
also in many areas of physics (evolution equations and propagation of a signal in an optical …

Starting from nonlocal symmetries related to Bäcklund transformation (BT), many interesting
results can be obtained. Taking the well-known potential KdV (pKdV) equation as an …

A variety of methods for examining the properties and solutions of nonlinear evolution
equations are explored by using the Vakhnenko equation (VE) as an example. The VE …

We develop the inverse scattering transform (IST) method for the Degasperis–Procesi
equation. The spectral problem is an Zakharov–Shabat problem with constant boundary …

The multisoliton solutions of the Degasperis–Procesi (DP) equation are constructed by
means of a reduction procedure (CKP reduction) for the multisoliton solutions of the …

Travelling-wave solutions of the Degasperis–Procesi equation are investigated. The
solutions are characterized by two parameters. For propagation in the positive x-direction …

We present a short history of the Ermakov Equation with an emphasis on its discovery by the
West and the subsequent boost to research into invariants for nonlinear systems although …