Complexiton solutions to the Korteweg–de Vries equation

Abstract A novel class of explicit exact solutions to the Korteweg–de Vries equation is presented through its bilinear form. Such solutions possess singularities of combinations of trigonometric function waves and exponential function waves which have different travelling speeds of new type. The functions used in the Wronskian determinants are derived from eigenfunctions of the Schrodinger spectral problem associated with complex eigenvalues, and thus the resulting solutions are called complexiton solutions. Illustrative examples of complexiton solutions are exhibited.

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