Group theoretic method for analyzing interaction of a weak discontinuity wave with a bore in shallow water waves

Abstract

A group theoretic method is used to establish the entire class of self-similar solutions to the problem of a bore as it approaches the shoreline on a sloping beach. Necessary conditions for the existence of similarity solutions for a bore are obtained. The results obtained compare well with the earlier results. A particular solution to the problem has been found, and used to study the interaction of the bore with a weak discontinuity.

Keywords:

• Bore
• Weak discontinuity
• Interaction of shock waves
• AMS Subject Classifications: 76D33
• 76E30

Notes

The author is very much grateful to Prof. V. D. Sharma, Department of Mathematics III, Bombay, India for his constant inspiration during the preparation of this work.

Additional information

Notes on contributors

J. Jena

The author is very much grateful to Prof. V. D. Sharma, Department of Mathematics III, Bombay, India for his constant inspiration during the preparation of this work.