A variational principle of the complex Hirota-dynamical model for optics

Finding the variational principle of the nonlinear partial differential equations (NPDEs) is called the inverse variational problem. Generally speaking, it is very difficult to establish the variational principle for the NPDEs. In this paper, the complex Hirota-dynamical model that takes a major role in the plasma and optical fibers is considered. The semi-inverse method (SIM) is adopted to develop the variational principle via constructing a trial-Lagrange function (TLF). Correspondingly, the Euler–Lagrange equation obtained by calculating the functional stationary condition is equivalent to the governing equation, thus proving the correctness of the established variational principle. As we all know, the variational principle is first explored by the SIM and can unveil some intrinsic connections between the different physical quantities.