D.E. Pelinovsky, J. Springael, F. Lambert and I. Loris

On modified NLS, Kaup and NLBq equations: differential transformations and bilinearization

J. Phys. A: Math. Gen. 30, 8705-8717 (1997)

Abstract:
New transformations between the nonlinear Schrodinger, Kaup and non-local Boussinesq equations as well as their modified counterparts are found and analysed. The bilinear representations of these equations, including an alternative bilinear form of the Chen-Lee-Liu equation, are obtained by a direct method based on the Bell's exponential polynomials. Explicit Wronskian solutions to these equations are also presented.

Keywords:
NONLOCAL BOUSSINESQ EQUATION, WATER-WAVE EQUATION, GAUGE TRANSFORMATIONS, SCHRODINGER EQUATION, SOLITON SOLUTIONS, INTEGRABLE HIERARCHIES