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It is known that an explosive instability can occur when nonlinear waves propagate in certain media that admit 3-wave mixing. The purpose of this Letter is to show that explosive instabilities can occur even in media that admit no 3-wave mixing. Instead, the instability is caused by 4-wave mixing: four resonantly interacting wave trains gain energy from a background, and all blowup in a finite time. Unlike singularities associated with self-focussing, these singularities can occur with no spatial structure-the waves blowup everywhere in space simultaneously. We have not yet investigated the effect of spatial structure on a 4-wave explosive instability. 相似文献
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Our purpose is to prove that the electron distribution function near a cathode in a weakly ionized heterogeneous medium has a “band structure” which disappears far from the cathode when an equilibrium state is attained. 相似文献
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An explicit, analytical model is presented of finite-amplitude waves in shallow water. The waves in question have two independent spatial periods, in two independent horizontal directions. Both short-crested and long-crested waves are available from the model. Every wave pattern is an exact solution of the Kadomtsev-Petviashvili equation, and is based on a Riemann theta function of genus 2. These biperiodic waves are direct generalizations of the well-known (simply periodic) cnoidal waves. Just as cnoidal waves are often used as one-dimensional models of “typical” nonlinear, periodic waves in shallow water, these biperiodic waves may be considered to represent “typical” nonlinear, periodic waves in shallow water without the assumption of one-dimensionality. 相似文献