Abstract:
It is shown that every one-dimensional differential operator whose coefficient functions
depend on an arbitrary set of parameters is associated with a series of multidimensional
nonlinear partial differential equations which can be integrated by means of the inverse
scattering problem method.
Citation:
V. E. Zakharov, S. V. Manakov, “Generalization of the inverse scattering problem method”, TMF, 27:3 (1976), 283–287; Theoret. and Math. Phys., 27:3 (1976), 485–487
\Bibitem{ZakMan76}
\by V.~E.~Zakharov, S.~V.~Manakov
\paper Generalization of the inverse scattering problem method
\jour TMF
\yr 1976
\vol 27
\issue 3
\pages 283--287
\mathnet{http://mi.mathnet.ru/tmf3330}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=457963}
\zmath{https://zbmath.org/?q=an:0334.47005}
\transl
\jour Theoret. and Math. Phys.
\yr 1976
\vol 27
\issue 3
\pages 485--487
\crossref{https://doi.org/10.1007/BF01028614}
Linking options:
https://www.mathnet.ru/eng/tmf3330
https://www.mathnet.ru/eng/tmf/v27/i3/p283
This publication is cited in the following 13 articles:
A. M. Samoilenko, Ya. A. Prykarpatsky, D. Blackmore, A. K. Prykarpatsky, “Theory of Multidimensional Delsarte–Lions Transmutation Operators. II”, Ukr Math J, 71:6 (2019), 921
V. H. Samoilenko, Yu. I. Samoilenko, “Asymptotic m-phase soliton-type solutions of a singularly perturbed Korteweg–de Vries equation with variable coefficients”, Ukr Math J, 64:7 (2012), 1109
Sergeev, SM, “Supertetrahedra and superalgebras”, Journal of Mathematical Physics, 50:8 (2009), 083519
A.I. Zenchuk, “Combination of Inverse Spectral Transform Method and Method of Characteristics: Deformed Pohlmeyer Equation”, JNMP, 15:supplement 3 (2008), 437
V. H. Samoilenko, Yu. I. Samoilenko, “Asymptotic solutions of the Cauchy problem for the singularly perturbed Korteweg-de Vries equation with variable coefficients”, Ukr Math J, 59:1 (2007), 126
Zenchuk, AI, “Multidimensional hierarchies of (1+1)-dimensional integrable partial differential equations. Nonsymmetric partial derivative-dressing”, Journal of Mathematical Physics, 41:9 (2000), 6248
A.I. Zenchuk, “On the dressing method in multidimension”, Physics Letters A, 277:1 (2000), 25
R.A. Kraenkel, M. Senthilvelan, A.I. Zenchuk, “Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa–Holm equation”, Physics Letters A, 273:3 (2000), 183
Marcus V Mesquita, Áurea R Vasconcellos, Roberto Luzzi, “Irreversible Processes in the Context of a Nonequilibrium Statistical Ensemble Formalism”, Phys. Scr., 59:4 (1999), 257
V. K. Mel'nikov, “Conservation laws for a class of systems of nonlinear evolution equations”, Funct. Anal. Appl., 15:1 (1981), 33–47
V. E. Zakharov, Topics in Current Physics, 17, Solitons, 1980, 243
V. E. Zakharov, A. B. Shabat, “Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II”, Funct. Anal. Appl., 13:3 (1979), 166–174
J.L. Gervais, A. Neveu, M.A. Virasoro, “Non-classical configurations in Euclidean field theory as minima of constrained systems”, Nuclear Physics B, 138:1 (1978), 45
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