# Higher-order energy expansions and spike locations

## Related Articles

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We study the following semilinear elliptic equation -?u + b(x)u = f(u), x ? RN, where b is periodic and f is assumed to be asymptotically linear. The purpose of this paper is to establish the existence of infinitely many homoclinic type solutions for this class of nonlinearities.

- Stationary Flow Past a Semi-Infinite Flat Plate: Analytical and Numerical Evidence for a Symmetry-Breaking Solution. Bichsel, Denis; Wittwer, Peter // Journal of Statistical Physics;Apr2007, Vol. 127 Issue 1, p133
We consider the question of the existence of stationary solutions for the Navier Stokes equations describing the flow of a incompressible fluid past a semi-infinite flat plate at zero incidence angle. By using ideas from the theory of dynamical systems we analyze the vorticity equation for this...

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We formulate a model to predict the shape of a stretched membrane which is nearly conformal to an underlying body and which is distorted by a small surface perturbation. We develop a number of models to examine the situation and obtain appropriate asymptotic approximations which are then...

- Asymptotic Expansions of Periodic Solutions for a Singular Perturbation Problem Including Nonlinear Dynamical System with Two Boundary Layers. Jahanshahi, M.; Mehri, B.; Aliev, N.; Sakai, K. // Southeast Asian Bulletin of Mathematics;2004, Vol. 28 Issue 1, p41
This paper is for the investigation and writing of asymptotic expansions of periodic solutions of a singular perturbation problem which includes a nonlinear dynamical system. One of the equations of this system includes small parameter Îµ. Supposing that boundary layers are formed at the both...

- ASYMPTOTICS OF SOLUTION FOR SINGULARLY PERTURBED NONLINEAR DISCRETE PERIODIC OPTIMAL CONTROL PROBLEMS. KURINA, GALINA; NEKRASOVA, NATALYA // Systems Science;2008, Vol. 34 Issue 1, p23
The asymptotic expansion of the solution of a singularly perturbed nonlinear discrete time periodic optimal control problem is constructed as series with respect to non-negative integer powers of a small parameter. The terms of asymptotic expansion are the solutions of optimal control problems...

- Approach to Equilibrium for the Phonon Boltzmann Equation. Bricmont, Jean; Kupiainen, Antti // Communications in Mathematical Physics;Jun2008, Vol. 281 Issue 1, p179
We study the asymptotics of solutions of the Boltzmann equation describing the kinetic limit of a lattice of classical interacting anharmonic oscillators. We prove that, if the initial condition is a small perturbation of an equilibrium state, and vanishes at infinity, the dynamics tends...

- Correlation energy extrapolation by intrinsic scaling. II. The water and the nitrogen molecule. Bytautas, Laimutis; Ruedenberg, Klaus // Journal of Chemical Physics;12/8/2004, Vol. 121 Issue 22, p10919
The extrapolation method for determining benchmark quality full configuration-interaction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules H2O and N2. As in the neon atom case, discussed in preceding paper [L....

- On convergence of gradient-dependent integrands. Martin Kru��k // Applications of Mathematics;Dec2007, Vol. 52 Issue 6, p529
Abstractï¿½ï¿½We study convergence properties of {?(?u k )}k?N if ? ? C(R m?m ), |?(s)| ? C(1+|s| p ), 1 p u k ? u weakly in W 1,p (O; R m ) and for some g ? C(O) it holds that ?O g(x)?(?u k (x))dx ? ?O g(x)Q?(?u(x))dx as k ? 8. In particular, we give necessary and sufficient...

- Rolling in the Higgs model and elliptic functions. Arefeva, I.; Volovich, I.; Piskovskiy, E. // Theoretical & Mathematical Physics;Jul2012, Vol. 172 Issue 1, p1001
Asymptotic methods in nonlinear dynamics such as, for example, the Krylov-Bogoliubov averaging method and the KAM theory are commonly used to improve perturbation theory results in the regime of small oscillations. But for a series of problems in nonlinear dynamics, in particular, for the Higgs...