this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

The aim of this paper is to obtain new necessary and sufficient conditions for the uniform exponential stability of variational difference equations with applications to robustness problems. We prove characterizations for exponential stability of variational difference equations using translation invariant sequence spaces and emphasize the importance of each hypothesis. We introduce a new conce...

Extending the approach of Grillakis–Shatah–Strauss, Bronski–Johnson–Kapitula, and others for Hamiltonian systems, we explore relations between the constrained variational problem minX:C(X)=c0 E(X), c0 ∈ R , and stability of solutions of a class of degenerate “quasi-gradient” systems dX/dt = −M∇E admitting constraints, including Cahn-Hilliard equations, oneand multi-dimensional viscoelasticity, ...

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy ...

Abstract In this paper, we propose an efficient approach to solve the fifthorder KdV equations. By using the variational iteration method, the exact solutions of the fifth-order KdV equations are given without the calculation of the complicated Adomian’s polynomials, linearization, discretization, weak nonlinearity assumptions or perturbation theory. Numerical examples are presented that show t...

In this paper, we introduce a computational method to find an approximate analytical solution for fuzzy differential equations. At first, variational iteration method (VIM) is used to solve the crisp problem then with the extension principle we find the fuzzy approximation solution. Examples are given , including linear and nonlinear fuzzy firstorder differential equations.

The applications of symmetry groups to problems arising in the calculus of variations have their origins in the late papers of Lie, e.g., [34], which introduced the subject of “integral invariants”. Lie showed how the symmetry group of a variational problem can be readily computed based on an adaptation of the infinitesimal method used to compute symmetry groups of differential equations. Moreo...