A Study On The B Family Of Shallow Water Wave Equations

Author

Snehanhsu Saha

Graduation Semester and Year

2008

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Yue Liu

Abstract

In this dissertation we study b family of shallow water wave equations which include classical Korteweg-de Vries, Camassa-Holm and Degasperis-Procesi equations. We first establish the models of the Camassa-Holm and Degasperis-Procesi equations, deriving them from the shallow waterwave argument and then compare a large class of properties relating to the two equations. Then we consider the b family equation as the parent equation and derive the above mentioned two equations as special cases of the b-family as well as the classical KdV equation.Next we establish results of local well-posedness using Kato's semigroup theory,global existence and blow up solutions under certain special initial profiles(periodic) and relate those to periodic b-family equation.Keywords:Camassa-Holm(CH) and Degasperis-Procesi(DP)equations; periodic b-family ;blow-up;local existence;global existence.

Disciplines

Mathematics | Physical Sciences and Mathematics

License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

Comments

Degree granted by The University of Texas at Arlington

Recommended Citation

Saha, Snehanhsu, "A Study On The B Family Of Shallow Water Wave Equations" (2008). Mathematics Dissertations. 8.
https://mavmatrix.uta.edu/math_dissertations/8