Determinant solutions to a (3+1)-dimensional generalized KP equation with variable coefficients

A system of linear conditions is presented for Wronskian and Grammian solutions to a (3+1)-dimensional generalized vcKP equation. The formulations of these solutions require a constraint on variable coefficients. © 2012 Fudan University and Springer-Verlag Berlin Heidelberg.Shanghai Leading Academic Discipline Project Natural Science Foundation of Shanghai: 09ZR1410800 National Natural Science Foundation of China: 61072147, 10831003, 11071159 State Administration of Foreign Experts Affairs University of South FloridaManuscript received November 26, 2011. Revised April 11, 2012. 1Department of Engineering Technology and Mathematics, Savannah State University, 3219 College Street, Savannah, Georgia 31404, USA. E-mail: alrazia@yahoo.com 2Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA. E-mail: mawx@cas.usf.cn 3Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA; Department of Mathematics, Ege University, 35100 Bornova-Izmir, Turkey. E-mail: ahmetyildirim80@gmail.com *Project supported by the State Administration of Foreign Experts Affairs of China, the National Natural Science Foundation of China (Nos. 10831003, 61072147, 11071159), the Shanghai Municipal Natural Science Foundation (No. 09ZR1410800) and the Shanghai Leading Academic Discipline Project (No. J50101). -- Acknowledgement The authors thank TUBITAK (the Scientific and Technological Research Council of Turkey) for its financial support and grant for the research entitled “Integrable Systems and Soliton Theory” at University of South Florida. -