Generalized variational principles of the Benjamin-Bona-Mahony-Peregrine-Burgers equation for nonlinear surface waves

Abstract The variational theory that widely used in many fields of mathematics, physics, engineering and control is a fundamental and important theory in mathematical physics. However, it is difficult to develop the variational principles of the nonlinear partial differential equations (NPDEs) in physics. In this work, we aim to establish the generalized variational principles of the Benjamin-Bona-Mahony-Peregrine-Burgers equation (BBMPBE) for nonlinear surface waves via employing the semi-inverse method (SIM). By this method, four different forms of the generalized variational principles are extracted. The whole deduction process is presented in detail. The extracted generalized variational principles in this research are expected to provide some new ideas and perspectives on the exploration of the variational method in physics.