ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A general class of Bäcklund transformations are considered for equations of the form izy+zxx+f(z,z¯)=0, where f(z,z¯) is a function of z=x+iy and z¯=x−iy. The nonlinear forms of this equation that admit such transformations are completely classified and shown to exist only when f(z,z¯)=z2z¯ (the nonlinear Schrödinger equation), z ln z¯, z ln z, (z+z¯)2, or suitable combinations of these functions. The form f(z,z¯)=(z+z¯)2 leads to auto-Bäcklund transformations for the Boussinesq equation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.529010
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