invariants of motion
Recently Published Documents


TOTAL DOCUMENTS

29
(FIVE YEARS 1)

H-INDEX

9
(FIVE YEARS 0)

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Chad E. Mitchell ◽  
Robert D. Ryne ◽  
Kilean Hwang ◽  
Sergei Nagaitsev ◽  
Timofey Zolkin

2019 ◽  
Vol 21 (11) ◽  
pp. 113024 ◽  
Author(s):  
Arnab Pal ◽  
Łukasz Kuśmierz ◽  
Shlomi Reuveni

2017 ◽  
Vol 14 (1) ◽  
pp. 800-806 ◽  
Author(s):  
K. R Raslan ◽  
Z. F Abu Shaeer

A finite element solution of the modified Korteweg-de Vries (MKdV) equation, based on Galerkin’s method using cubic splines as element shape functions, is set up. A linear stability analysis shows the scheme is unconditionally stable. Numerical tests for single, two and three solitons are used to assess the performance of the proposed scheme. The four invariants of motion are evaluated to determine the conservation properties of the algorithm.


2016 ◽  
Vol 5 (2) ◽  
pp. 123 ◽  
Author(s):  
K. R. Raslan ◽  
Talaat S. El-Danaf ◽  
Khalid K. Ali

In the present paper, a numerical method is proposed for the numerical solution of a coupled system of KdV (CKdV) equation with appropriate initial and boundary conditions by using collocation method with quintic B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms, are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.


2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Zhengyong Ouyang

We consider the orbital stability of solitary traveling wave solutions of an equation describing the free surface waves of moderate amplitude in the shallow water regime. Firstly, we rewrite this equation in Hamiltonian form and construct two invariants of motion. Then using the abstract stability theorem of solitary waves proposed by Grillakis et al. (1987), we prove that the solitary traveling waves of the equation under consideration are orbital stable.


2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Liquan Mei ◽  
Yali Gao ◽  
Zhangxin Chen

A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.


2011 ◽  
Vol 57 (3) ◽  
pp. 609-616 ◽  
Author(s):  
Samir Hamdi ◽  
Brian Morse ◽  
Bernard Halphen ◽  
William Schiesser

2009 ◽  
Vol 19 (10) ◽  
pp. 3473-3484 ◽  
Author(s):  
C. M. SARRIS ◽  
ARACELI N. PROTO

We describe how, departing from the Shannon entropy, it is possible to deal with semiquantum time-independent nonlinear Hamiltonians. The interplay between the quantal and classical degrees of freedom can be easily seen, and the set of differential equations that govern the temporal evolution of the quantal mean values and the classical variables is obtained. We find invariants of motion and, particularly, we describe under which conditions, the uncertainty principle remains as an invariant of motion too. Through the analysis of these invariants, it is possible to follow the transition of the system from quantum to classical regime and to conclude that the uncertainty principle behaves as an indicator telling us whether the system is in regular or irregular regime. A simple example is shown.


Sign in / Sign up

Export Citation Format

Share Document