Hysteresis in the nonlinear driven drift and KdV equations |
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| Institution: | 1. Department of Immunobiology, Yale University School of Medicine, New Haven, CT, 06520 USA;2. Program in Integrative Cell Signaling and Neurobiology of Metabolism, Section of Comparative Medicine, Yale University School of Medicine, New Haven, CT, 06520 USA;3. Department of Laboratory Medicine, Yale University School of Medicine, New Haven, CT, 06520 USA;4. Department of Neurosurgery, Yale University School of Medicine, New Haven, CT, 06520 USA;5. Department of Microbial Pathogenesis, Yale University School of Medicine, New Haven, CT, 06520 USA;6. Howard Hughes Medical Institute, Yale University School of Medicine, New Haven, CT, 06520 USA;1. Department of energy, CIEMAT, Avda. Complutence 40, 28040 Madrid, Spain;2. University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA |
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| Abstract: | The nonlinear driven/damped differential equation ∂φ/∂t+a∂3φ/∂t∂2y+b∂3φ/∂3y+c∂φ/∂y+fφ∂φ/∂y= −ϵ sin (Ky-ωt)−γφ with a=0 (KdV equation) or b=0 (drift equation) is numerically studied in a parameter region where the energy tends to a constant, Es, for t→∞. It is found that Es(ϵ) traces a hysteresis curve when the driving amplitude ϵ is cyclically varied. |
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