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First, I thank God for His grace, mercy and peace. He gave me everything I have, and He made me everything I am. It is a pleasure to express my sincere appreciation to my advisor, Prof. Michael Mudi Tom. Without his invaluable advice, help and guidance, this dissertation would not be completed. I also like to thank him for introducing me to the Kadomtsev-Petviashvili Equations. He has been extremely generous with his in-sight and knowledge. I also like to thank the committee members, Prof. Jimmie Lawson, Prof. Frank Neubrander, Prof. Augusto Nobile, Prof., Li-yeng Sung and Prof. George Voyiadjis. I thank everyone in the Department of Mathematics for their help throughout my time at LSU. They provided me with a very pleasant environment for working and studying. To my fellow graduate students, I am very grateful for all your friendship, support and care. Special thanks goes to Dr. Carolyn Chun, she is a friend, sister and trusted companion, may God remember her for good and never forgets her labor of love. Julius Esunge is a friend that sticks closer than a brother