A STUDY ON THE B FAMILY OF SHALLOW WATER WAVE EQUATIONS

I would like to thank my supervising professor Dr. Yue Liu for constantly moti-vating and encouraging me, and also for his invaluable advice during the course of my doctoral studies. I wish to thank my academic advisors Dr. Gaik,Ambartsoumian, Dr. Hristo,Kojouharov, Dr. Li, Ren-Cang,Li and Dr. Guojun,Liao, for their interest in my research and for taking time to serve in my dissertation committee. I would also like to extend my appreciation to Department of Mathematics,University of Texas @ Arlington for providing financial support for my doctoral studies. I am especially grateful to Dr. James K.Peterson,my masters ’ advisor for his interest in my research and for the helpful discussions and invaluable comments. I am grateful to all the teachers who taught me during the years I spent in school, in India and in the Unites States. I would like to thank Dr. Eleanor Jenkins, Dr. Ruth Gornet and Dr. Jianzhong,Su for encouraging and inspiring me throughout my graduate studies. Finally, I would like to express my deep gratitude to my wife,Swati Routh, who have encouraged and inspired me and been so supportive through the entire period. I am extremely fortunate to be so blessed. I am also extremely grateful to my family for their sacrifice, encouragement and patience. A special thanks goes out to my best friends Subhobrato and Rajib. Thank you for believing in me