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Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II. (English. Russian original) Zbl 0448.35090
Funct. Anal. Appl. 13, 166-174 (1980); translation from Funkts. Anal. Prilozh. 13, No. 3, 13-22 (1979).

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35R30 Inverse problems for PDEs
81T08 Constructive quantum field theory
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References:
[1] P. D. Lax, ”Integrals of nonlinear evolution equations and solitary waves,” Matematika13, No. 5, 128–150 (1969).
[2] V. E. Zakharov and L. D. Faddeev, ”The KdV equation – a completely integrable Hamiltonian system,” Funkts. Anal.,5, No. 4, 18–27 (1971).
[3] M. G. Ablowitz, D. G. Kaup, A. C. Newell, and H. Segur, ”The inverse scattering transform – Fourier analysis for nonlinear problems,” Stud. Appl. Math.,53, 249–277 (1974). · Zbl 0408.35068
[4] V. E. Zakharov and A. B. Shabat, ”A scheme for integrating nonlinear equations of mathematical physics by the method of the inverse scattering problem,” Funkts. Anal.,8, No. 3, 54–56 (1974). · Zbl 0303.35024
[5] F. Calogero, ”A method to generate solvable nonlinear evolution equations,” Lett. Nuovo Cimento,14, 443–449 (1975).
[6] F. Calogero and A. Degasperis, ”Nonlinear evolution equations solvable by the inverse spectral transform. I,” Nuovo Cimento,32B, 201 (1976). · Zbl 0406.35056
[7] V. E. Zakharov and S. V. Manakov, ”On generalization of the method of the inverse scattering problem,” Teor. Mat. Fiz.,27, No. 3, 283–287 (1976). · Zbl 0413.47006
[8] V. E. Zakharov and S. V. Manakov, ”On the resonance interaction of wave packets in nonlinear media,” Pis’ma Zh. Eksp. Teor. Fiz.,18, No. 7, 413–447 (1973).
[9] K. Pohlmeyer, ”Integrable Hamiltonian systems and interactions through quadric constraints,” Commun. Math. Phys.,46, 207–221 (1976). · Zbl 0996.37504
[10] V. E. Zakharov and A. V. Mikhailov, ”Relativistically invariant systems integrable by the method of the inverse scattering problem,” Zh. Eksp. Teor. Fiz.,74, No. 6, 1953–1973 (1978).
[11] A. A. Belavin and V. E. Zakharov, ”A higher-dimensional method of the inverse scattering problem and the duality equation for the Yang–Mills field,” Pis’ma Zh. Eksp. Teor. Fiz.,25, No. 12, 603–607 (1977).
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