Nonlinear evolution equations solvable by the inverse spectral transform.

Nonlinear evolution equations solvable by the inverse spectral transform.—I

Published:1976-04 Issue:2 Volume:32 Page:201-242
ISSN:1826-9877
Container-title:Il Nuovo Cimento B Series 11
language:en
Short-container-title:Nuov Cim B

Author:

Calogero F.,Degasperis A.

Publisher

Springer Science and Business Media LLC

Subject

General Medicine

Link

http://link.springer.com/content/pdf/10.1007/BF02727634.pdf

Reference32 articles.

1. Throughout this paper whenever we mention NLPDE’s we include also the possibility that these be integro-differential equations (that may, or may not, reduce to pure partial differential equations, possibly by an appropriate redefinition of the dependent variable).

2. C. S. Gardner, J. M. Greene, M. D. Kruskal andR. M. Miura:Phys. Rev. Lett.,19, 1095 (1967);Comm. Pure Appl. Math.,27, 97 (1974).

3. Out of the extensive literature on this topic we list here only the most significant contributions, selected on the basis of their review nature, their landmark character or their technical closeness to the approach of this paper;a)G. C. Scott, F. Y. F. Chu andD. W. McLaughlin:Proc. IEEE,61, 1443 (1973);b)G. B. Whitham:Linear and Nonlinear Waves (New York, N. Y., 1974);c)J. Moser, Editor:Dynamical Systems, Theory and Applications (Berlin, 1974) (see in particular the papers byM. Kruskal and byH. Flaschka andA. C. Newell);d)P. D. Lax:Comm. Pure Appl. Math.,21, 467 (1968);e)V. E. Zakharov andL. D. Faddeev:Func. Anal. Appl.,5, 280 (1971);f)V. E. Zakharov andA. B. Shabat:Sov. Phys. JETP,34, 62 (1972);g)M. J. Ablowitz, D. J. Kaup, A. C. Newell andH. Segur:Stud. Appl. Math.,53, 249 (1974), hereafter referred to as AKNS;h)F. Calogero:Lett. Nuovo Cimento,14, 443 (1965);i)T. Kotera andK. Sawada:Journ. Phys. Soc. Japan,39, 501 (1975). Presumably another useful reference, that we have however not yet been able to consult, isNonlinear Wave Motion, edited byA. C. Newell,Lectures in Applied Math.,15 (Providence, R. I., 1974).

4. We list again only a few contributions, particularly significant in the context of this paper:H. D. Wahlquist andF. B. Estabrook:a)Phys. Rev. Lett.,31, 1386 (1973);b) Journ. Math. Phys.,16, 1 (1975);c)D. W. McLaughlin andA. C. Scott:Journ. Math. Phys.,14, 1817 (1973);d)G. L. Lamb jr.:Journ. Math. Phys.,15, 2157 (1974);e)F. Calogero:Lett. Nuovo Cimento,14, 537 (1975); see also the papers of ref. (3) Out of the extensive literature on this topic we list here only the most significant contributions, selected on the basis of their review nature, their landmark character or their technical closeness to the approach of this paper:a)A. C. Scott, F. Y. F. Chu andD. W. McLaughlin:Proc. IEEE,61, 1443 (1973);b)G. B. Whitham:Linear and Nonlinear Waves (New York, N. Y., 1974);c)J. Moser, Editor:Dynamical Systems, Theory and Applications (Berlin, 1974) (see in particular the papers byM. Kruskal and byH. Flaschka andA. C. Newell);d)P. D. Lax:Comm. Pure Appl. Math.,21, 467 (1968);e)V. E. Zakharov andL. D. Faddeev:Func. Anal. Appl.,5, 280 (1971);f)V. E. Zakharov andA. B. Shabat:Sov. Phys. JETP,34, 62 (1972);g)M. J. Ablowitz, D. J. Kaup, A. C. Newell andH. Segur:Stud. Appl. Math.,53, 249 (1974), hereafter referred to as AKNS;h)F. Calogero:Lett. Nuovo Cimento,14, 443 (1965);i)T. Kotera andK. Sawada:Journ. Phys. Soc. Japan,39, 501 (1975). Presumably another useful reference, that we have however not yet been able to consult, isNonlinear Wave Motion, edited byA. C. Newell,Lectures in Applied Math.,15 (Providence, R. I., 1974).

5. D. J. Korteweg andG. DeVries:Phil. Mag.,39, 422 (1895).

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