Solitary waves in a class of generalized Korteweg–de Vries equations
Solitary waves in a class of generalized Korteweg–de Vries equations
We study the class of generalized Korteweg--de Vries (KdV) equations derivable from the Lagrangian: L(l,p) =F[1/2${\mathit{cphi}}_{\mathit{x}}$${\mathit{cphi}}_{\mathit{t}}$ -(${\mathit{cphi}}_{\mathit{x}}$${)}^{\mathit{l}}$/l(l-1) +\ensuremath{\alpha}(${\mathit{cphi}}_{\mathit{x}}$${)}^{\mathit{p}}$(${\mathit{cphi}}_{\mathit{x}\mathit{x}}$${)}^{2}$]dx, where the usual fields u(x,t) of the generalized KIdV equation are defined by u(x,t)=${\mathit{cphi}}_{\mathit{x}}$(x,t). This class contains compactons, which are solitary waves with compact support, and when l=p+2, these solutions have the …