zbMATH — the first resource for mathematics

Conservation laws for a class of systems of nonlinear evolution equations. (English. Russian original) Zbl 0523.35088
Funct. Anal. Appl. 15, 33-47 (1981); translation from Funkts. Anal. Prilozh. 15, No. 1, 43-60 (1981).

35Q99 Partial differential equations of mathematical physics and other areas of application
35L65 Hyperbolic conservation laws
35R15 PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables)
Full Text: DOI
[1] C. S. Gardner, J. M. Green, M. D. Kruskal, and R. M. Miura, ”Method for solving the KdV equation,” Phys. Rev. Lett.,19, No. 19, 1095-1097 (1967). · Zbl 1103.35360 · doi:10.1103/PhysRevLett.19.1095
[2] I. A. Kunin, Theory of Elastic Media with Microstructure [in Russian], Nauka, Moscow (1975). · Zbl 0557.73093
[3] B. A. Dubrovin, V. B. Matveev, and S. P. Novikov, ”Nonlinear equations of Korteweg?de Vries type, finite-band linear operators, and Abelian varieties,” Usp. Mat. Nauk,31, No. 1, 55-136 (1976). · Zbl 0326.35011
[4] P. Lax, ”Integrals of nonlinear equations of evolution and solitary waves,” Commun. Pure Appl. Math.,21, No. 5, 467-490 (1968). · Zbl 0162.41103 · doi:10.1002/cpa.3160210503
[5] M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, ”Nonlinear evolution equations of physical significance,” Phys. Rev. Lett.,31, No. 2, 125-127 (1973). · Zbl 1243.35143 · doi:10.1103/PhysRevLett.31.125
[6] V. E. Zakharov and A. B. Shabat, ”A scheme of interpolation of nonlinear equations of mathematical physics by the methods of the inverse scattering problem. I,” Funkts. Anal. Prilozhen.,8, No. 3, 43-53 (1974). · Zbl 0303.35024
[7] V. E. Zakharov and S. V. Manakov, ”On a generalization of the method of inverse problem,” Teor. Mat. Fiz.,27, No. 3, 283-287 (1976).
[8] I. M. Krichever, ”Methods of algebraic geometry in the theory of nonlinear equations,” Usp. Mat. Nauk,32, No. 6, 183-208 (1977). · Zbl 0372.35002
[9] I. M. Gel’fand and L. A. Dikii, ”The asymptotic of the resolvent of the Sturm?Liouville equations and the algebra of the Korteweg?de Vries equations,” Usp. Mat. Nauk,30, No. 5, 67-100 (1975). · Zbl 0334.58007
[10] I. M. Gel’fand and L. A. Dikii, ”Fractional powers of operators and Hamiltonian systems,” Funkts. Anal. Prilozhen.,10, No. 4, 13-39 (1976).
[11] I. M. Gel’fand and L. A. Dikii, ”Resolvent and Hamiltonian systems,” Funkts. Anal. Prilozhen.,11, No. 2, 11-27 (1977).
[12] I. M. Gel’fand and L. A. Dikii, ”Computation of jets and nonlinear Hamiltonian systems,” Funkts. Anal. Prilozhen.,12, No. 2, 8-23 (1978).
[13] V. K. Mel’nikov, ”On the equations that are generated by an operator relation,” Mat. Sb.,108, 378-392 (1979).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.