Mathematical Sciences: Study of Model Equations For Water Waves

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9622858 Chen The investigator will study various Boussinesq systems which describe the two-way propagation of water waves in nonlinear, dispersive media. Boussinesq systems with various approximate dissipative terms will also be studied theoretically and numerically. Generally speaking, all the issues studied for the famous KdV-equation, which describes waves traveling in one direction, should be investigated. The major goal for this project is to decide which system of equations and which dissipative mechanism is best suited for the modeling of physical problems in fluid mechanics. The ideal system should at least be mathematically sound, physically correct, have the least complexity, and can be used to simulate a wide range of real water wave problems.