Prog. Theor. Phys. Vol. 58 No. 1 (1977) pp. 161-174
Spectrum Method for a General Evolution Equation
Department of Engineering Mathematics, Faculty of Engineering, Utsunomiya University, Utsunomiya 321-31
(Received January 8, 1977)
Inverse scattering method is investigated for a general class of evolution equations. A decisive role is played by a transformation operator from the solution of the evolution equation to the eigenfunction for an operator with eigenvalues constant in time. Classes of the evolution equations with the same spectrum problem are presented and a generalization of the Fourier transform method to the nonlinear equation is suggested. The theory is applied to the several evolution equations including the Burgers equation and the vector equation studied by Ablowitz and others.
DOI : 10.1143/PTP.58.161
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Citing Article(s) :
Journal of the Physical Society of Japan 59 (1990) pp. 3791-3792
On a Miura Map for Ito's Equation
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Progress of Theoretical Physics Vol. 74 No. 5 (1985) pp. 1005-1012
Recursion Operators for N×N Matrix Nonlinear Evolution Equations
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