Kaup, D. J. Finding eigenvalue problems for solving nonlinear evolution equations. (English) Zbl 1079.37509 Prog. Theor. Phys. 54, No. 1, 72-78 (1975). Summary: The problem of determining what nonlinear evolution equations are exactly solvable by inverse scattering techniques is simplified by considering a linear limit. By linearizing a given eigenvalue problem and the associated time evolution operator, it is possible to determine the class of linearized dispersion relation(s) of the exactly solvable nonlinear evolution equations. Examples are given to illustrate the method. Cited in 16 Documents MSC: 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 35Q55 NLS equations (nonlinear Schrödinger equations) 35P25 Scattering theory for PDEs 35G20 Nonlinear higher-order PDEs 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs PDF BibTeX XML Cite \textit{D. J. Kaup}, Prog. Theor. Phys. 54, No. 1, 72--78 (1975; Zbl 1079.37509) Full Text: DOI OpenURL