On Periodic Water-Waves and Their Convergence to Solitary Waves in the Long-Wave Limit.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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A detailed discussion of Nekrasovs approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of 1 to show the global convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasove leads, via the Maximum Principle, to new results about qualitative features of periodic waves, for which there has long been a global existence theory 9, 12. Author
- Theoretical Mathematics