Evolution equation for bidirectional surface waves in a convecting fluid

Surface waves in a heated viscous fluid exhibit a long wave oscillatory instability. The nonlinear evolution of unidirectional waves is known to be described by a modified Korteweg-deVries-Kuramoto-Sivashinsky equation. In the present work we eliminate the restriction of unidirectional waves and find that the evolution of the wave is governed by a modified Boussinesq system . A perturbed Boussinesq equation of the form $y_{tt}-y_{xx} -\epsilon^2(y_{xxtt} + (y^2)_{xx})+ \epsilon^3(y_{xxt}+y_{xxxxt} + (y^2)_{xxt}) =0$ which includes instability and dissipation is derived from this system.Comment: 8 pages, no figure

Speed of field driven domain walls in nanowires with large transverse magnetic anisotropy

Recent analytical and numerical work on field driven domain wall propagation in nanowires has shown that for large transverse anisotropy and sufficiently large applied fields the Walker profile becomes unstable before the breakdown field, giving way to a slower stationary domain wall. We perform an asymptotic expansion of the Landau Lifshitz Gilbert equation for large transverse magnetic anisotropy and show that the asymptotic dynamics reproduces this behavior. At low applied field the speed increases linearly with the field and the profile is the classic Landau profile. Beyond a critical value of the applied field the domain wall slows down. The appearance of a slower domain wall profile in the asymptotic dynamics is due to a transition from a pushed to a pulled front of a reaction diffusion equation.Comment: 8 page

Variational calculation of the period of nonlinear oscillators

The problem of calculating the period of second order nonlinear autonomous oscillators is formulated as an eigenvalue problem. We show that the period can be obtained from two integral variational principles dual to each other. Upper and lower bounds on the period can be obtained to any desired degree of accuracy. The results are illustrated by an application to the Duffing equation.Comment: 7 page

Phase Space Derivation of a Variational Principle for One Dimensional Hamiltonian Systems

We consider the bifurcation problem u'' + \lambda u = N(u) with two point boundary conditions where N(u) is a general nonlinear term which may also depend on the eigenvalue \lambda. A new derivation of a variational principle for the lowest eigenvalue \lambda is given. This derivation makes use only of simple algebraic inequalities and leads directly to a more explicit expression for the eigenvalue than what had been given previously.Comment: 2 pages, Revtex, no figure