The nonlinear coupling of three wave packets is solved for interactions either evolving in time and one-dimensional space or occurring in steady state in two dimensions. Solutions are given using the inverse-scattering technique and numerical integration of the differential equations.

The methods of statistical mechanics are used to evaluate sums of many-vertex Feynman graphs in a simple quantum-field-theory model.

We rigorously prove that in three or more dimensions, the nearest-neighbor, simple-cubic, ferromagnetic, quantum Heisenberg model of spin $S(=\frac{1}{2}, 1, \dots )$ has a phase transition at nonzero temperature.

Exponential instability of waves on the cubically nonlinear, one-dimensional lattice is considered. The lattice has been modeled by the modified Korteweg-de Vries (mKdV) equation. It is shown that some solutions of the mKdV equation are unstable, and that these mKdV instabilities correspond to the instabilities observed on the lattice. Such instabilities may be important in determining whether or not a system behaves stochastically.

We use a current-current model for weak interactions to show that the weak-interaction contribution to the ground state energies of typical nuclei is about a part in ${10}^8$ of their rest masses. By comparing this contribution with the results of the recent versions of the Eötvös experiments, we conclude that weak-interaction energies obey the principle of equivalence to better than a part in 100, thus refuting claims that those experiments did not test weak-interaction effects.

In two experiments in 1974 and 1975, utilizing a radio interferometer of 35-km base-line, the relative positions of three radio sources were monitored over a period of a month when the sun was within 10 deg of the sources. The mean gravitational deflection is 1.007 ± 0.009 (standard error) times the value predicted by general relativity. These results exclude the Brans-Dicke theory of gravitation with a scalar coupling constant $\omega <23\mathrm{}$ at the 99% confidence level.

We show that classical sine-Gordon solitons maintain their integrity to a high degree in the presence of external perturbations. Two examples, of particular importance in condensed matter, are described in detail: (i) A model impurity is found to bind low-velocity solitons but merely phase shift those with high velocities, and (ii) external static driving terms with damping accelerate the soliton to a terminal velocity. The importance of a translation mode is emphasized and it is concluded that the soliton behaves as a classical particle in all essential respects.

The coefficients in the Callan-Symanzik equations for a three-dimensional, continuous spin Ising model with an $\exp (-A{s}^4+B{s}^2)$ spin-weight factor are expanded in the dimensionless, renormalized coupling constant. These series are summed by the Padé-Borel method to yield the critical indices $\gamma =1.241\mathrm{}\pm 0.002$, $\eta =0.02\mathrm{}\pm 0.02$, $\nu =0.63\mathrm{}\pm 0.01$, and ${\Delta }_1=0.49\mathrm{}\pm 0.01$.

An experiment was performed to search for the anomalous two-photon polarization correlation observed earlier by Holt and Pipkin using a cascade of atomic mercury. The experiment is a sensitive test of various aspects of the foundations of quantum mechanics. Although the present experimental arrangement differed only slightly from theirs, the anomalous results were not observed.

Using two models, we study the relaxation to a Maxwell distribution in the context of classical kinetic theory. For the first model, an exact solution of the nonlinear Boltzmann equation is derived. For the second model, an asymptotic solution exhibits the remarkable feature of a transient tail population sometimes much larger than the equilibrium Maxwell distribution. This phenomenon may be of importance for calculating rates of fast chemical reactions and for controlled thermonuclear fusion.

This paper presents a new and generally covariant approach to quantum field theory in curved space-time. Previously unknown expressions are obtained for particle creation amplitudes in oscillating gravitational fields. These expressions illuminate the physical origin of the particle creation.

The shape of the large, random clusters, occurring near percolation threshold $c_0$, is shown to be such that the mean cluster boundary-to-bulk ratio $\frac{〈b〉}{〈n〉}$ gives $c_0$. A Monte Carlo calculation yields that the cluster size distribution is proportional to a Gaussian in $\frac{b}{n}$ which is independent of concentration and narrows to a $\delta$ function as $n\to \infty$; the asymptotic behavior gives $c_0$ and the critical exponents.

The past and present observable properties of the Sun have been theoretically calculated on the assumption that the gravitational constant $G$ increases or decreases with time. Consideration of Davis's experimental upper limit on the present solar neutrino flux and of terrestial paleontological data sets a limit on the absolute rate of change of $G$, namely, $\left|\frac{{\dot{G}}_0}{G_0}\right|<\mathrm{}1\mathrm{}\times {10}^{-10\mathrm{}}/\mathrm{yr}$, if other standard constants do not also change with time.

The prolongation structure of Wahlquist and Estabrook is interpreted as a connection. In this way, some geometric insight might be provided for the description of those nonlinear partial differential equations which admit soliton solutions. A new geometric property—linked to the existence of an $\mathrm{SL}(2, R)$ connection—is proved for the solutions of the Korteweg-de Vries equation.

The nonlinear $\sigma$ model is renormalizable and asymptotically free in two dimensions. We show here how to construct this model in $2+\epsilon$ dimensions. Renormalization-group equations follow and exhibit a nontrivial uv stable fixed point, which corresponds in the language of Heisenberg ferromagnets to a critical point. The existence of systematic expansions in powers of $d-2\mathrm{}$ follows from this analysis. In the presence of a source information about long-distance behavior above the critical coupling constant is obtainable.

In 1918, Lense and Thirring calculated that a moon orbiting a rotating planet would experience a nodal dragging effect due to general relativity. We describe an experiment to measure this effect to 1% with two counter-orbiting drag-free satellites in polar earth orbit. In addition to tracking data from existing ground stations, satellite-to-satellite Doppler ranging data are taken near the poles. New geophysical information is inherent in the polar data.

An analysis of six years of lunar-laser-ranging data gives a zero amplitude for the Nordtvedt term in the Earth-Moon distance yielding the Nordtvedt parameter $\eta =0.00\mathrm{}\pm 0.03$ Thus, Earth's gravitational self-energy contributes equally, ±3%, to its inertial mass and passive gravitational mass. At the 70% confidence level this result is only consistent with the Brans-Dicke theory for $\omega >29\mathrm{}$. We obtain $|\beta -1|\lesssim 0.02 \mathrm{to} 0.05$ for five-parameter parametrized post-Newtonian theories of gravitation with energy-momentum conservation, or $|\beta -1|\lesssim 0.01$ if only $\beta$ and $\gamma$ are considered.

Analysis of 1389 measurements, accumulated between 1970 and 1974, of echo delays of laser signals transmitted from Earth and reflected from cube corners on the Moon shows gravitational binding energy to contribute equally to Earth's inertial and passive gravitational masses to within the estimated uncertainty of 1.5%. The corresponding restriction on the Eddington-Robertson parameters is $4\beta -\gamma -3=-0.001\mathrm{}\pm 0.015$. Combination with other results, as if independent, yields $\beta =1.003\mathrm{}\pm 0.005$ and $\gamma =1.008\mathrm{}\pm 0.008$, in accord with general relativity.

The question of $C$, $P$, and $T$ nonconservation in gravity is reexamined, and feasible experiments are suggested to test these effects.

A new approximant is proposed for the critical correlation function $g\left(y\right)\mathrm{}$ of $y=k\xi$, where $\xi$ is the correlation length and $k$ the wave number of an order-parameter fluctuation. The approach involves truncating the spectral function associated with the three-term Fisher-Langer approximant in a manner suggested by the requirement of a three-particle threshold. The resulting $g\left(y\right)\mathrm{}$ is accurate to better than 0.03% everywhere for the two-dimensional Ising model. Results for the three-dimensional case are consistent with $\epsilon$-expansion and high-temperature series results.