A generalized inf–sup stable variational formulation for the wave equation

Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

Construction of a solitary wave solution for the generalized Zakharov equation by a variational iteration method

In this paper, the well-known He’s variational iteration method (VIM) is used to construct solitary wave solutions for the generalized Zakharov equation (GZE). The chosen initial solution (trial function) can be in soliton form with some unknown parameters, which can be determined in the solution procedure. c © 2007 Elsevier Ltd. All rights reserved.

A Variational Formulation for the Navier-stokes Equation

The variational formulation of the Fokker-Planck equation : a summary

Generalized traveling-wave method, variational approach, and modified conserved quantities for the perturbed nonlinear Schrödinger equation.

The generalized traveling wave method (GTWM) is developed for the nonlinear Schrödinger equation (NLSE) with general perturbations in order to obtain the equations of motion for an arbitrary number of collective coordinates. Regardless of the particular ansatz that is used, it is shown that this alternative approach is equivalent to the Lagrangian formalism, but has the advantage that only the ...