TITLE

Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation

AUTHOR(S)
D. Bonheure; L. Sanchez; M. Tarallo; S. Terracini
PUB. DATE
August 2003
SOURCE
Calculus of Variations & Partial Differential Equations;Aug2003, Vol. 17 Issue 4, p341
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Assuming that f is a potential having three minima at the same level of energy, we study for the conservative equation $$ u�{iv}-g(u)u��>-\frac{1}{2}g'(u)u'�2+f'(u)=0,$$ the existence of a heteroclinic connection between the extremal equilibria. Our method consists in minimizing the functional $$\int_{-\infty}�{+\infty}\left[\frac{1}{2}[(u��>{}�2)+g(u)u'{}�2]+f(u)\right] dx$$ whose Euler-Lagrange equation is given by (1), in a suitable space of functions.
ACCESSION #
10498927

 

Related Articles

  • Optical solitons as quantum objects. Pomeau, Yves; Le Berre, Martine // Chaos;Sep2007, Vol. 17 Issue 3, p037118 

    The intensity of classical bright solitons propagating in linearly coupled identical fibers can be distributed either in a stable symmetric state at strong coupling or in a stable asymmetric state if the coupling is small enough. In the first case, if the initial state is not the equilibrium...

  • An inexact logarithmic-quadratic proximal augmented Lagrangian method for a class of constrained variational inequalities. Li, M.; Shao, H.; He, B. S. // Mathematical Methods of Operations Research;2007, Vol. 66 Issue 2, p183 

    The augmented Lagrangian method is attractive in constraint optimizations. When it is applied to a class of constrained variational inequalities, the sub-problem in each iteration is a nonlinear complementarity problem (NCP). By introducing a logarithmic-quadratic proximal term, the sub-NCP...

  • Relativistic Lagrange formulation. Geroch, Robert; Nagy, G.; Reula, O. // Journal of Mathematical Physics;Aug2001, Vol. 42 Issue 8 

    It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial differential equations. These include numerous systems of...

  • Quadrupolar ordering of phospholipid molecules in narrow necks of phospholipid vesicles. Kralj-Iglič, Veronika; Babnik, Blaž; Gauger, Dorit; May, Sylvio; Iglič, Aleš // Journal of Statistical Physics;Nov2006, Vol. 125 Issue 3, p723 

    Shapes of phospholipid vesicles that involve narrow neck(s) were studied theoretically. It is taken into account that phospholipid molecules are intrinsically anisotropic with respect to the membrane normal and that they exhibit quadrupolar orientational ordering according to the difference...

  • Molecular dynamics integration and molecular vibrational theory. I. New symplectic integrators. Janežič, Dušanka; Praprotnik, Matej; Merzel, Franci // Journal of Chemical Physics;5/1/2005, Vol. 122 Issue 17, p174101 

    New symplectic integrators have been developed by combining molecular dynamics integration with the standard theory of molecular vibrations to solve the Hamiltonian equations of motion. The presented integrators analytically resolve the internal high-frequency molecular vibrations by introducing...

  • A variational principle motivated by the optional rod theory. Atanackovic, T.M.; Vujanovic, B.D.; Baclic, B.S. // Acta Mechanica;2000, Vol. 139 Issue 1-4, p57 

    Demonstrates that a number of well-known nonlinear second order differential equations appearing in theoretical physics provide the necessary condition for the minimum of the functional variational principles. View that second-order differential equations as conservation laws for the...

  • Particle motion in vorticity-conserving, two-dimensional incompressible flows. Brown, Michael G.; Samelson, Roger M. // Physics of Fluids;Sep94, Vol. 6 Issue 9, p2875 

    It is shown that particle motion is integrable in any vorticity-conserving, two-dimensional incompressible flow if the vorticity is a differentiable function whose gradient never vanishes. More generally, the result is true if any Lagrangian invariant replaces the vorticity.

  • On Lagrange's Theorem with Prime Variables. JIANYA LIU // Quarterly Journal of Mathematics;Dec2003, Vol. 54 Issue 4, p453 

    It is conjectured that Lagrange's theorem on four squares is true for prime variables, that is, every large integer n with n = 4 (mod 24) is the sum of four squares of primes. In this paper, the size for the exceptional set in the above conjecture is reduced to O(N2/5+e). The new ingredients...

  • SPECIAL LAGRANGIAN CONES IN $\C^3$ AND PRIMITIVE HARMONIC MAPS. IAN McINTOSH // Journal of the London Mathematical Society;Jun2003, Vol. 67 Issue 3, p769 

    It is shown that every special Lagrangian cone in $\C^3$ determines, and is determined by, a primitive harmonic surface in the 6-symmetric space ${\rm SU}_3/{\rm SO}_2$. For cones over tori, this allows the classification theory of harmonic tori to be used to describe the...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics