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Compactons; $\mathcal{PT}$ symmetry; generalized KdV equations.

This paper considers the $\mathcal{PT}$-symmetric extensions of the equations examined by Cooper, Shepard and Sodano. From the scaling properties of the $\mathcal{PT}$-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.

Carl M Bender¹ Fred Cooper^{2 3} Avinash Khare⁴ Bogdan Mihaila⁵ Avadh Saxena³

1. Department of Physics, Washington University, St. Louis, MO 63130, USA
2. National Science Foundation, Division of Physics, Arlington, VA 22230, USA and Santa Fe Institute, Santa Fe, NM 87501, USA
3. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
4. Institute of Physics, Sachivalaya Marg, Bhubaneswar 751 005, India
5. Material Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Published

August 2009