
Computing Travelling Wave Solutions (TWS) for nonlinear PDE systemsEdgardo ChebTerrab, MITACSCECM, SFUMonday Feburary 9th, 2004, in K9509 at 3:30pm.
Given a nonlinear PDE system in unknowns f[i](x[j]), a travelling wave solution is an exact closed form solution of the form n[i]  \ k f[i](tau) = ) A[i, k] tau /  k = 1 where the n[i] are finite, the A[i,k] are constants with respect to the independent variables x[j], and j  \ tau = tanh( ) C[k] x[k]) /  k = 1 where the C[k] are constants with respect to the x[j]. This type of solution plays an important role in the study of nonlinear physical phenomena (fluid dynamics, elastic media, field theories etc.). In this talk the way TWS are constructed is reviewed (includes a demo of a Maple implementation), the generality of these solutions is analyzed and a generalization of the method taking tau as the solution of an arbitrary Riccati equation is discussed. 