Bäcklund transformations for generalized nonlinear Schrödinger equations
Date
1990Source
Journal of Mathematical PhysicsVolume
31Issue
11Pages
2597-2602Google Scholar check
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A general class of Bäcklund transformations are considered for equations of the form izy + zxx + f(z,z̄) = 0, where f(z,z̄) is a function of z = x + iy and z̄ = x - iy. The nonlinear forms of this equation that admit such transformations are completely classified and shown to exist only when f(z,z̄) = z2z̄ (the nonlinear Schrödinger equation), z ln z̄, z ln z, (z + z̄)2, or suitable combinations of these functions. The form f(z,z̄) = (z + z̄)2 leads to auto-Bäcklund transformations for the Boussinesq equation. © 1990 American Institute of Physics.