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