@article{oai:toyama.repo.nii.ac.jp:00004400,
 author = {川田, 勉},
 journal = {富山大学工学部紀要},
 month = {Mar},
 note = {It is interesting to seek the simplest way solving nonlinear evolution equations (NLEE). A contribution by Crum should be emphasized, where a simple way of potential proliferation had given for the one-dimensional Schrodinger operator and the resulting potential is characterized by a parameter. Wadati et al had pointed out that is applicable for the Backlund transformation (BT) solving the integrable NLEE. We thought Crum's method well comparable to a version of Riemann-Hilbert transform (RHT) except for the contribution from continuous scattering data.
Recently various kinds of transformations have been studied for integrable NLEE's. Our hope is to arive at such a situation based on the RHT. Along this thema we specially show a crucial point for deriving the BT in this note.
Discussions are given generally as possible. Based on the RHT, we derive a general and direct potential proliferation by using a projection matrix. The proliferation formula generally solves soliton solutions, but we distinguish this from the BT. according to Alberty et al, we derive
the Riccati equation and change the RHT as suitable for description of the associated transformation between solutions of Riccati eqs. The resulting transformation includes, a "singular" one and we find it playing a kee role for deriving the BT. For examples the two-dimensional M X M-AKNS class of NLEE's is discussed and we show how to eliminate the Riccati solution from the transformation., Article, 富山大学工学部紀要，40},
 pages = {171--180},
 title = {Direct Potential Proliferation, Connection with the Riccati Equation and Related Transformation},
 volume = {40},
 year = {1989}
}