Computing Travelling Wave Solutions (TWS) for non-linear PDE systems
Edgardo Cheb-Terrab, MITACS-CECM, SFUMonday Feburary 9th, 2004, in K9509 at 3:30pm.
Given a non-linear 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 non-linear 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.