Reduction technique for matrix nonlinear evolution equations

Author:

Degasperis A.

Publisher

Springer Berlin Heidelberg

Reference15 articles.

1. GARDNER, C.S., GREENE, J.M., KRUSKAL, M.D., MIURA, R.M.: “Method for solving the Korteweg-de Vries equation”. Phys. Rev. Lett. 19, 1095–1097 (1967).

2. a) ZAKHAROV, V.E., SHABAT, A.B.: “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media”. Sov. Phys. JETP 34, 62–69 (1972) [Zh.Eksp.Teor.Fiz. 161, 118(1971); b) ABLOWITZ, M.J., KAUP, D.J., NEWELL, A.C., SEGUR, H.: “The inverse scattering transform-Fourier analysis for nonlinear problems”. Studies Appl.Math. 53, 249–315(1974); c) CALOGERO, F., DEGASPERIS, A.: “Nonlinear evolution equations solvable by the inverse spectral transform, I”. Nuovo Cimento 32B, 201–242 (1976); d) CALOGERO, F., DEGASPERIS, A.: “Nonlinear evolution equations solvable by the inverse spectral transform, II”. Nuovo Cimento 39B, 1–54(1977); NEWELL; A.C.: “The general structure of integrable evolution equations”. Proc. R. Soc. Lond. A 365, 283–311(1979) CALOGERO, F., DEGASPERIS, A.: “Extension of the Spectral Transform method for solving nonlinear evolution equations, I & II”. Lett.Nuovo Cimento 22, 131–137(1978) & 22, 263–269(1978); CALOGERO, F., DEGASPERIS, A.: “Solution by the Spectral Transform method of a nonlinear evolution equation including as a special case the Cylindrical KdV Equation”. Lett. Nuovo Cimento 23, 150–154(1978).

3. BULLOUGH, R.K., CAUDREY, P.J.: “The soliton and its history” in “Solitons” (Bullough R.K. and Caudrey, P.J., eds), Lecture Notes in Physics, Springer, Heidelberg, 1979; and also references quoted there.

4. WADATI, M., KAMIJO, T.: “On the extension of inverse scattering method”. Prog. Theor.Phys. 52, 397–414 (1974). Ref. (2-d). ZAKHAROV, V.E.:“The inverse scattering method”, in “Solitons” (Bullough, R.K. and Caudrey, P.J., eds.), Lecture Notes in Physics, Springer, Heidelberg, 1979.

5. CALOGERO, F., DEGASPERIS, A.: “Reduction technique for matrix nonlinear evolution equations solvable by the Spectral Transform”. To appear in J. of Math.Phys.

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Phase Space Analysis for the Direct Algebraic Method for Nonlinear Evolution and Wave Equations;SIAM Journal on Applied Mathematics;1992-08

2. On Series Expansions Giving Closed-Form Solutions of Korteweg–de Vries-Like Equations;SIAM Journal on Applied Mathematics;1990-12

3. Spectral Transform and Solitons: How to Solve and Investigate Nonlinear Evolution Equations;Order and Chaos in Nonlinear Physical Systems;1988

4. Hamiltonian structure of the general integrable equations under reductions;Physica D: Nonlinear Phenomena;1985-04

5. References;Studies in Mathematics and Its Applications;1982

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