On Periodic Water-Waves and Their Convergence to Solitary Waves in the Long-Wave Limit.

Amick, C. J.; Toland, J. F.

On Periodic Water-Waves and Their Convergence to Solitary Waves in the Long-Wave Limit.

Active / Technical Report | Accession Number: ADA093610 |

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Abstract:

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

Author(s):

Amick, C. J. ; Toland, J. F.

Author Organization(s):

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Descriptive Note:

Technical summary rept.,

Pagination:

0077

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:

Approved For Public Release

RECORD

Collection: TR

Identifying Numbers

Report Number(s):

MRC-TSR-2127

Contract/Grant Number(s):

DAAG29-80-C-0041

Subject Terms

Joint Capability Areas:

JCA_1.2_Force Preparation; JCA_1_Force Support; JCA_1.2.3_Educating; JCA_1.2.5_Lessons Learned; JCA_5_Command and Control; JCA_5.3_Planning

Communities of Interest:

Air Platforms

Descriptor(s):

*INTEGRAL EQUATIONS, *WAVE EQUATIONS, VELOCITY, STEADY STATE, WATER WAVES, EIGENVECTORS, EIGENVALUES, CONVERGENCE, OPERATORS(MATHEMATICS), AMPLITUDE, ASYMPTOTIC NORMALITY, PERIODIC FUNCTIONS, THEOREMS

Field(s)/Group(s):

Theoretical Mathematics

Report Date:

1980 Oct 01