PT-Symmetric Extension of the Korteweg-de Vries Equation
Abstract
The Korteweg-de Vries equation ut+uux+uxxx=0 is PT symmetric (invariant under space-time reflection). Therefore, it can be generalized and extended into the complex domain in such a way as to preserve the PT symmetry. The result is the family of complex nonlinear wave equations ut-iu(i ux)epsilon+uxxx=0, where epsilon is real. The features of these equations are discussed. Special attention is given to the epsilon=3 equation, for which conservation laws are derived and solitary waves are investigated.
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