in this paper, the variational iteration method proposed by ji-huan he is applied to solve both linear and nonlinear schrodinger equations. the main property of the method is in its flexibility and ability to solve linear and nonlinear equations accurately and conveniently. in this method, general lagrange multipliers are introduced to construct correction functionals to the problems. the multi...

Abstract This paper is devoted to discrete mechanical systems subject external forces. We introduce a version of with Rayleigh-type forces, obtain the equations motion and characterize equivalence for these systems. Additionally, we Noether’s theorem other characterizing Lie subalgebra symmetries forced Lagrangian system. Moreover, develop Hamilton–Jacobi theory Hamiltonian These results are us...

The Crank–Nicolson scheme as well as its modified schemes is widely used in numerical simulations for the nonlinear Schrödinger equation. In this paper, we prove the multisymplecticity and symplecticity of this scheme. Firstly, we reconstruct the scheme by the concatenating method and present the corresponding discrete multisymplectic conservation law. Based on the discrete variational principl...

Structure-preserving numerical schemes for a nonlinear parabolic fourthorder equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation formula (BDF) semi-discretization in time is investigated. The scheme preserves the nonnegativity of the solution, is entropy stable and dissipates a modified e...

VARIATIONAL THEORY: VARIABLE-INDEPENDENCE AND CONSISTENCY Jian-zhong Zhao Geophysics Department, College of Resource, Environment and Earth Sciences, Yunnan University, Kunming, P.R. China 650091 [email protected] Abstract Variational theory of elasticity is surveyed in the context of mathematical logic in the present paper. The problem of variable-independence of variational principles ra...

Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides molecular surface and structural representation, and offers the basis for molecular visualization, which is crucial for the understanding of molecular structure a...

We study variational problems for curves approximated by B-spline curves. We show that one can obtain discrete Euler-Lagrange equations for the data describing the approximated curves. Our main application is to the occluded curve problem in 2D and 3D. In this case, the aim is to find various aesthetically pleasing solutions as opposed to a solution of a physical problem. The Lagrangians of int...

We study the existence of multiple nontrivial solutions for nonlinear fourth order discrete boundary value problems. first establish criteria at least two problems and obtain conditions to guarantee that are sign-changing. Under some appropriate assumptions, we further prove have three solutions, which positive, negative, sign-changing, respectively. include examples illustrate applicability ou...

We construct discrete analogues of Dirac structures by considering the geometry of symplectic maps and their associated generating functions, in a manner analogous to the construction of continuous Dirac structures in terms of the geometry of symplectic vector fields and their associated Hamiltonians. We demonstrate that this framework provides a means of deriving implicit discrete Lagrangian a...

Variational integrators are symplectic-momentum preserving integrators that are based on a discrete variational formulation of the underlying system. So far, variational integrators have been mainly developed and used for a wide variety of mechanical systems. In this work, we develop a variational integrator for the simulation of electric circuits. An appropriate variational formulation is pres...