This revised and updated second edition of a highly successful book is the only text at this level to embrace a universal approach to three major developments in classical physics; namely nonlinear waves, solitons and chaos. The authors now include new material on biology and laser theory, and go on to discuss important recent developments such as soliton metamorphosis. A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures. Each chapter concludes with a set of problems. This text will be particularly valuable for students taking courses in nonlinear aspects of physics. In general, it will be of value to final year undergraduates and beginning graduate students studying fluid dynamics, plasma physics and applied mathematics.

Abstract. The power law dependence of the power spectrum of auroral indices, and in-situ magnetic field observations in the earth's geotail, may be evidence that the coupled solar wind-magnetospheric system exhibits scale free self organised criticality and can to some extent be described by avalanche models. In contrast, the intensity of, and time interval between, substorms both have well defined probability distributions with characteristic scales. We present results from a simple cellular automaton that models avalanches in a one dimensional "sandpile"; here we examine the simplest case of constant inflow. This model generates a probability distribution of energy discharges due to internal reorganization that is a power law implying SOC, whereas systemwide discharges (flow of "sand" out of the system) form a distinct group which do not exhibit SOC. The energy dissipated in a systemwide discharge follows a probability distribution with a well defined mean, as does the time interval between one systemwide discharge and the next. Internal and external avalanches can therefore in principle be identified with distinct processes in the dynamic geotail. If so, the avalanche model places restrictions on the class of physical process that may be invoked to explain the observed geomagnetic dynamics.

Swarming is a conspicuous behavioral trait observed in bird flocks, fish shoals, insect swarms, and mammal herds. It is thought to improve collective awareness and offer protection from predators. Many current models involve the hypothesis that information coordinating motion is exchanged among neighbors. We argue that such local interactions alone are insufficient to explain the organization of large flocks of birds and that the mechanism for the exchange of long-range information necessary to control their density remains unknown. We show that large flocks self-organize to the maximum density at which a typical individual still can see out of the flock in many directions. Such flocks are marginally opaque-an external observer also still can see a substantial fraction of sky through the flock. Although this seems intuitive, we show it need not be the case; flocks might easily be highly diffuse or entirely opaque. The emergence of marginal opacity strongly constrains how individuals interact with one another within large swarms. It also provides a mechanism for global interactions: an individual can respond to the projection of the flock that it sees. This provides for faster information transfer and hence rapid flock dynamics, another advantage over local models. From a behavioral perspective, it optimizes the information available to each bird while maintaining the protection of a dense, coherent flock.flocking | collective motion S tarling murmurations represent one of the most impressive examples of organization in the natural world, with flocks of up to 300,000 individuals or more able to coordinate themselves into a cohesive and highly coherent group (1-5).Although the primary source of sensory information to a bird is visual, it would be unrealistic to expect that individual to recognize and track the position and orientation of a significant proportion of the other members of a flock (3, 4). Indeed, observations on real starling flocks show that a bird responds to this type of information only from its seven nearest neighbors and that these interactions are scale-free (1, 5, 6). Local interactions such as this are enough to create order within a flock (5-10) but do not give any information on the state of the flock as a whole, nor do they explain how density might be regulated. Most models use attraction and repulsion interactions, use a fictitious potential field, or simply fix the available volume to control the density (6)(7)(8)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20).To make progress, we first ask a simple question: "What does a bird actually see when it is part of a large flock?" Its view out from within a large flock likely would present the vast majority of individuals merely as silhouettes, moving too fast and at too great a distance to be tracked easily or even discriminated from one another. Here the basic visual input to each individual is assumed to be based simply on visual contrast: a dynamic pattern of dark (bird) and light (sky) across the field of vision (although it might be possible to...

For certain combinations of temperature and magnetic field, the evolution with time of the magnetization of some phase-separated manganese oxides exhibits a unique steplike feature. This jump in the magnetization is proposed to correspond to a burstlike growth of the ferromagnetic fraction at the expense of the antiferromagnetic component, driven by the evolution of the strains at the interfaces between the two kinds of domains. These results bear a striking similarity with the phenomenon of an ''incubation time'' encountered in standard martensitic transformations.