The Short Pulse Hierarchy
نویسنده
چکیده
We study a new hierarchy of equations containing the Short Pulse equation, which describes the evolution of very short pulses in nonlinear media, and the Elastic Beam equation, which describes nonlinear transverse oscillations of elastic beams under tension. We show that the hierarchy of equations is integrable. We obtain the two compatible Hamiltonian structures. We construct an infinite series of both local and nonlocal conserved charges. A Lax description is presented for both systems. For the Elastic Beam equations we also obtain a nonstandard Lax representation.
منابع مشابه
Unique Solution of Short Pulse Propagation in Nonlinear Fiber Bragg Grating
In this study, a new numerical method is introduced to obtain the exact shape of output pulse in the chalcogenide fiber Bragg grating (FBG). A Gaussian pulse shape with 173 ps width is used as an input pulse for lunching to a 6.6 mm nonlinear FBG. Because of bistable and hysteresis nature of nonlinear FBG the time sequence of each portion of pulse is affected the shape of output pulse. So we di...
متن کاملNonlocal thermoelastic semi-infinite medium with variable thermal conductivity due to a laser short-pulse
In this article, the thermoelastic interactions in an isotropic and homogeneous semi-infinite medium with variable thermal conductivity caused by an ultra-short pulsed laser heating based on the linear nonlocal theory of elasticity has been considered. We consider that the thermal conductivity of the material is dependent on the temperature. The surface of the surrounding plane of the medium is...
متن کاملInter-pulse Interval Affects the Size of Single-pulse TMS-induced Motor Evoked Potentials: a Reliability Study
Introduction: Measuring the size of motor evoked potentials (MEPs) induced by transcranial magnetic stimulation (TMS) is an investigational technique to show the level of corticospinal excitability however, some of the fundamental methodological aspects of TMS (such as the effects of inter-pulse intervals (IPI) on MEP size) are not fully understood, this issue raises concerns about the re...
متن کاملAugmentation of paired pulse index as short-term plasticity due to morphine dependence
Abstract* Introduction: Chronic morphine exposure can cause addiction and affect synaptic plasticity, but the underlying neural mechanisms of this phenomenon remain unknown. Herein we used electrophysiologic approaches in hippocampal CA1 area to examine the effect of chronic morphine administration on short-term plasticity. Methods: Experiments were carried out on hippocampal slices taken f...
متن کاملEffects of Neonatal C-Fiber Depletion on Interaction between Neocortical Short-Term and Long-Term Plasticity
Introduction: The primary somatosensory cortex has an important role in nociceptive sensory-discriminative processing. Altered peripheral inputs produced by deafferentation or by long-term changes in levels of afferent stimulation can result in plasticity of cortex. Capsaicin-induced depletion of C-fiber afferents results in plasticity of the somatosensory system. Plasticity includes short-term...
متن کامل