Exact elliptic compactons in genepalized Kopteweg-De Pies equations

Using the action principle, and assuming a solitary wave of the generic form u(x, t) = AZ(beta (x + q(t)), we derive a general theorem relating the energy, momentum, and velocity of any solitary wave solution of the generalized Korteweg-De Vries equation K* (1, p). Specifically we find that 4 = r(l, p)H/P, where l, p are nonlinearity parameters. We also relate the amplitude, width, and momentum to the velocity of these solutions. We obtain the general condition for linear and Lyapunov stability We then obtain a two-parameter family of exact solutions to these equations, which include elliptic and hyper-elliptic compacton solutions. For this general family we explicitly verify both the theorem and the stability criteria. (c) 2006 Wiley Periodicals, Inc.