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Application of hereditary symmetries to nonlinear evolution equations. (English) Zbl 0419.35049

35G10Initial value problems for linear higher-order PDE
35K25Higher order parabolic equations, general
35R99Miscellaneous topics involving PDE
35Q99PDE of mathematical physics and other areas
Full Text: DOI
[1] Yamamuro, S.: Differential calculus in topological linear spaces. Lecture notes in mathematics 374 (1974) · Zbl 0276.58001
[2] Wadati, M.: Invariances and conservation laws of the Korteweg-de Vries equation. Stud. appl. Math. 59, 153-186 (1978) · Zbl 0386.35039
[3] Magri, F.: A simple model of the integrable Hamiltonian equation. J. math. Phys. 19, 1156-1162 (1978) · Zbl 0383.35065
[4] Lax, P. D.: Integrals of nonlinear equations of evolution and solitary waves. Communs pure appl. Math. 21, 467-490 (1968) · Zbl 0162.41103
[5] Fuchssteiner, B.: Pure soliton solutions of some nonlinear partial differential equations. Communs math. Phys. 55, 187-194 (1977) · Zbl 0361.35018
[6] Ames, W. F.: Nonlinear partial differential equations in engineering. (1965) · Zbl 0176.39701
[7] Gardner, C. S.; Greene, J. M.; Kruskal, M. D.; Miura, R. M.: Korteweg-de Vries equation and generalizations VI. Methods for exact solution. Communs pure appl. Math. 27, 97-133 (1974) · Zbl 0291.35012
[8] Lax, P. D.: Almost periodic solutions of the KdV-equation. SIAM rev. 18, 351-375 (1976) · Zbl 0329.35015
[9] Miura, R. M.: The Korteweg--de Vries equation: A survey of results. SIAM rev. 18, 412-459 (1976) · Zbl 0333.35021
[10] Zakharov, V. E.; Shabat, B. A.: Exact theory of two-dimensional self-focusing and one-dimensional self modulation of waves in nonlinear media. Soviet phys. JETP 34, 62-69 (1972)
[11] Ablowitz, M. J.; Kaup, D. J.; Newell, A. C.; Segur, H.: The inverse scattering transform-Fourier analysis for nonlinear problems. Stud. appl. Math. 53, 249-315 (1974) · Zbl 0408.35068
[12] Zhiber, A. V.: Conservation laws for the equation utt - $uxx + sin(u) = 0$. Funktiosional’nyi analiz i ego prilozheniya 11, 65-66 (1977)
[13] Ablowitz, M. J.; Kaup, D. J.; Newell, A. C.; Segur, H.: Nonlinear evolution equations of physical significance. Phys. rev. Letters 31, 125-127 (1973) · Zbl 1243.35143
[14] Kruskal, M. D.: The Korteweg--de Vries equation and related evolution equations. Am. math. Soc. 15, 61-84 (1974) · Zbl 0292.35017
[15] Kruskal, M. D.; Zabusky, N. J.: Interaction of solutions in a collisionless plasma and the recurrence of initial states. Phys. rev. Letters 15, 240-243 (1965) · Zbl 1201.35174
[16] Miura, R. M.: Korteweg--de Vries equation and generalizations I. A remarkable explicit nonlinear transformation. J. math. Phys. 9, 1202-1204 (1968) · Zbl 0283.35018