Happy Birthday, Jerry! Friend, Mentor and Colleague

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Happy Birthday, Jerry!Happy Birthday, Jerry!

Friend, Mentor and Colleague Friend, Mentor and Colleague

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Hongqiu CHEN, J. BONA, O. Karakashian

University of Memphis

Poitiers, June 10, 2011

Coupled KdV-systems of equations: well-Coupled KdV-systems of equations: well-posdness, posdness,

explicit solitary-wave solutions and their explicit solitary-wave solutions and their stability stability

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Mathematical & Physical CriteriaMathematical & Physical Criteria

1.1. Well-posedWell-posed

linearly, nonlinearly locally, globallylinearly, nonlinearly locally, globally2.2. Preserves ‘Energy’Preserves ‘Energy’3.3. Has Has Solitary WavesSolitary Waves

existence, stability of solitary wavesexistence, stability of solitary waves4.4. Comparison with the full equations of motionComparison with the full equations of motion

on long time scaleson long time scales5.5. Qualitative & Quantitative agreement with Qualitative & Quantitative agreement with

ExperimentsExperiments

in the laboratory and with field in the laboratory and with field

observationsobservations

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THANK YOU!THANK YOU!

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