# On the complete integrability of a nonlinear Schrödinger equation

@article{Zakharov1974OnTC, title={On the complete integrability of a nonlinear Schr{\"o}dinger equation}, author={V. E. Zakharov and S. Manakov}, journal={Theoretical and Mathematical Physics}, year={1974}, volume={19}, pages={551-559} }

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#### References

SHOWING 1-3 OF 3 REFERENCES

Method for solving the Korteweg-deVries equation

- Physics
- 1967

A method for solving the initial-value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as… Expand