Exact elliptic compactons in generalized Korteweg–De Vries equations

Using the action principle, and assuming a solitary wave of the generic form u ( x , t ) = AZ (β( 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 *( l , p ). Specifically we find that ${\dot q}=r(l,p)H/P$ , 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. © 2006 Wiley Periodicals, Inc. Complexity 11: 30–34, 2006