A Darboux Transformation for Ito Equation

Using a direct test function based on the Hirota’s bilinear form, two classes of mixed type exact solutions to the (2[Formula: see text]+[Formula: see text]1)-dimensional Ito equation are found through symbolic computations with Mathematica. These mixed type exact solutions contain exponential function, trigonometric function and hyperbolic function. The physical structures and characteristics for these resulting mixed type exact solutions are illustrated by some three-dimensional plots and contour plots.

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A Darboux Transformation for Ito Equation

Abstract: A system proposed by Ito is reconsidered. The corresponding Darboux transformation is presented explicitly. The resulted Bäcklund transformation is shown to be equivalent to the one found by Hirota. Also, a nonlinear superposition formula, which is of differential-algebraic, is obtained.

Cited by 2 publications

References 11 publications

Comment on ‘two new integrable fourth-order nonlinear equations: multiple soliton solutions and multiple complex soliton solutions’

Comment on ‘two new integrable fourth-order nonlinear equations: multiple soliton solutions and multiple complex soliton solutions’

Mixed type exact solutions to the (2+1)-dimensional Ito equation

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