Compactons in PT-symmetric generalized

Korteweg--de Vries equations

CARL M BENDER¹, FRED COOPER^2,5, AVINASH KHARE^3,*,

BOGDAN MIHAILA⁴ and AVADH SAXENA⁵

¹Department of Physics, Washington University, St. Louis, MO 63130, USA

²National Science Foundation, Division of Physics, Arlington,

VA 22230, USA and

Santa Fe Institute, Santa Fe, NM 87501, USA

³Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India

⁴Material Science and Technology Division, Los Alamos National

Laboratory, Los Alamos, NM 87545, USA

⁵Theoretical Division and Center for Nonlinear Studies, Los

Alamos National Laboratory, Los Alamos, NM 87545, USA

^*Corresponding author. E-mail: khare@iopb.res.in

Abstract. This paper considers the PT-symmetric extensions

of the equations examined by Cooper, Shepard and Sodano. From the

scaling properties of the PT-symmetric equations a general

theorem relating the energy, momentum and velocity of any

solitary-wave solution of the generalized KdV equation is derived.

We also discuss the stability of the compacton solution as a

function of the parameters affecting the nonlinearities.

Keywords. Compactons; PT symmetry; generalized KdV

equations.

PACS Nos 03.65.Ge; 02.60.Lj; 11.30.Er; 52.35.Sb