Nonlinear Waves Seminar - Alexei Cheviakov
| Wednesday, May 18, 2016 3:00 PM - 4:00 PM |
| Main Campus - Engineering Office Tower - 226: Applied Math Conference Room Main Campus - Engineering Classroom Wing - 257: Newton Lab |
| Alexei Cheviakov, Department of Mathematics and Statistics, University of Saskatchewan, Canada Exact Solutions of a Fully Nonlinear Two-Fluid Model The nonlinear Choi-Camassa model is an asymptotic approximate PDE model describing large-amplitude long internal waves in a horizontal channel containing two non-mixing fluid layers. Asymptotic assumptions of this model and its relationship with Euler equations are discussed. An equivalence transformation leading to a special dimensionless form of the system is derived; it reduces the number of constant physical parameters in the model from five to one. The Choi-Camassa model admits traveling wave solutions. For that ansatz, a dimensionless ordinary differential equation is derived. It is shown to admit several multi-parameter families of exact closed-form solutions. These traveling wave solutions hold for an arbitrary wave speeds, and correspond to periodic, solitary, and kink-type bidirectional traveling waves of the Choi-Camassa model. |