Abstract
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.
Similar content being viewed by others
References
Hirota, R., The direct method in soliton theory, Cambridge Tracts in Maohematics, Vol. 155, Cambridge University Press, Cambridge, 2004.
Hietarinta, J., Hirota’s bilinear method and soliton solutions, Phys. AUC, 15(1), 2005, 31–37.
Ma, W. X., Huang, T. W. and Zhang, Y., A multiple exp-function method for nonlinear differential equations and its application, Phys. Scr., 82, 2010, 065003.
Ma, W. X. and Fan, E. G., Linear superposition principle applying to Hirota bilinear equations, Comput. Math. Appl., 61, 2011, 950–959.
Ma, W. X., Zhang, Y., Tang, Y. N., et al., Hiota bilinear equations with linear subspaces of solutions, Appl. Math. Comput., 218, 2012, 7174–7183.
Satsuma, J., A Wronskian representation of N-soliton solutions of nonlinear evolution equations, J. Phys. Soc. Jpn., 46, 1979, 359–360.
Matveev, V. B., Positon-positon and soliton-positon collisions: KdV case, Phys. Lett. A, 166, 1992, 200–212.
Ma, W. X., Complexiton solutions to the Korteweg-de Vries equation, Phys. Lett. A, 301, 2002, 35–44.
Ma, W. X. and Maruno, K., Complexiton solutions of the Toda lattice equation, Physica A, 343, 2004, 219–237.
Ma, W. X., Soliton, positon and negaton solutions to a Schrödinger self-consistent source equation, J. Phys. Soc. Jpn., 72, 2003, 3017–3019.
Ma, W. X., Complexiton solutions of the Korteweg-de Vries equation with self-consistent sources, Chaos, Solitons Fractals, 26, 2005, 1453–1458.
Nakamura, A., A bilinear N-soliton formula for the KP equation, J. Phys. Soc. Jpn., 58, 1989, 412–422.
Hirota, R., Soliton solutions to the BKP equations — I. The Pfaffian technique, J. Phys. Soc. Jpn., 58, 1989, 2285–2296.
Ma, W. X., Abdeljabbar, A. and Assad, M. G., Wronskian and Grammian solutions to a (3+1)-dimensional generalized KP equation, Appl. Math. Comput., 217, 2011, 10016–10023.
Wazwaz, A. M., Multiple-soliton solutions for a (3+1)-dimensional generalized KP equation, Commun. Nonlinear Sci. Numer. Simu., 17, 2012, 491–495.
Ma, W. X. and Abdeljabbar, A., A bilinear Bäcklund transformation of a (3+1)-dimensional generalized KP equation, Appl. Math. Lett., 25, 2012, 1500–1504.
Ma, W. X. and Pekcan, A., Uniqueness of the Kadomtsev-Petviashvili and Boussinesq equations, Z. Naturforsch. A., 66, 2011, 377–382.
You, F. C., Xia, T. C. and Chen, D. Y., Decomposition of the generalized KP, cKP and mKP and their exact solutions, Phys. Lett. A, 372, 2008, 3184–3194.
Hirota, R., A new form of Bäcklund transformations and its relation to the inverse scattering problem, Progr. Theoret. Phys., 52, 1974, 1498–1512.
Author information
Authors and Affiliations
Corresponding author
Additional information
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).
Rights and permissions
About this article
Cite this article
Abdeljabbar, A., Ma, W. & Yildirim, A. Determinant solutions to a (3+1)-dimensional generalized KP equation with variable coefficients. Chin. Ann. Math. Ser. B 33, 641–650 (2012). https://doi.org/10.1007/s11401-012-0738-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11401-012-0738-8