Field theories that describe small fluctuations of branes are limits of 'brane theories' that describe large fluctuations. In particular, supersymmetric sigma-models arise in this way. These lectures discuss the soliton solutions of the associated 'brane theories' and their relation to calibrations. The last five years or so have seen some exciting developments in high energy/gravitational phys...

Field theories that describe small fluctuations of branes are limits of 'brane theories' that describe large fluctuations. In particular, supersymmetric sigma-models arise in this way. These lectures discuss the soliton solutions of the associated 'brane theories' and their relation to calibrations. The last five years or so have seen some exciting developments in high energy/gravitational phys...

the compressibility factor of nonassociated chain molecules composed of hard convex core yukawa segments was derived with saft-vr and an extension of the barker-henderson perturbation theory for convex bodies. the temperature-dependent chain and dispersion compressibility factors were derived using the yukawa potential. the effects of temperature, packing fraction, and segment number on the com...

In this work, we consider the stability of solitons for the KdV equation below the energy space, using spatially-exponentiallyweighted norms. Using a combination of the I-method and spectral analysis following Pego and Weinstein, we are able to show that, in the exponentially weighted space, the perturbation of a soliton decays exponentially for arbitrarily long times. The finite time restricti...

The mathematical description of localized solitons in the presence large-scale waves is a fundamental problem nonlinear science, with applications fluid dynamics, optics, and condensed matter physics. Here, evolution soliton as it interacts rarefaction wave or dispersive shock wave, examples slowly varying rapidly oscillating mean fields, for Korteweg–de Vries equation studied. Step boundary co...

We present a novel $n$EPT ($n$th-order Eulerian Perturbation Theory) scheme to model the nonlinear density field by summation up $n$th-order fields in perturbation theory. The obtained analytical power spectrum shows excellent agreement with results from all 20 Dark-Quest suites of $N$-body simulations spreading over broad range cosmologies. is much better than conventional two-loop Standard Th...

We consider the existence and stability of the hole, or dark soliton, solution to a Ginzburg–Landau perturbation of the defocusing nonlinear Schrödinger equation (NLS), and to the nearly real complex Ginzburg–Landau equation (CGL). By using dynamical systems techniques, it is shown that the dark soliton can persist as either a regular perturbation or a singular perturbation of that which exists...