Algebraic aspects of nonlinear differential equations

@article{Manin1979AlgebraicAO,
  title={Algebraic aspects of nonlinear differential equations},
  author={Yu. I. Manin},
  journal={Journal of Soviet Mathematics},
  year={1979},
  volume={11},
  pages={1-122}
}
  • Y. Manin
  • Published 1979
  • Mathematics
  • Journal of Soviet Mathematics
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226 Citations
Highly Influential Citations
10
Background Citations
36
Methods Citations
16
Results Citations
1

226 Citations

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References

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Hill’s Operator and Hyperelliptic Function Theory in the Presence of Infinitely Many Branch Points
\(C_{1}^{k},\,k \leq \infty \), is the class of k times continuously differentiable real-valued functions of period 1. Q denotes the Hill’s operator − d2∕dx2 + q(x) with a fixed q of class…
The soliton: A new concept in applied science
The term soliton has recently been coined to describe a pulselike nonlinear wave (solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed. To date at least…
A Variety of Nonlinear Network Equations Generated from the Bäcklund Transformation for the Toda Lattice
A Backlund transformation in the bilinear form is presented for the Toda equation. The Backlund transformation generates an important class of nonlinear evolution equations that exhibits N-soliton…
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The Korteweg–deVries Equation: A Survey of Results
The Korteweg–de Vries equation \[ u_t + uu_x + u_{xxx} = 0\] is a nonlinear partial differential equation arising in the study of a number of different physical systems, e.g., water waves, plasma…
On the complete integrability of the two-dimensional classical Thirring model
Topological Charges in Field Theory
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Korteweg-de Vries equation: A completely integrable Hamiltonian system
Essentially nonlinear one-dimensional model of classical field theory
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