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

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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.

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References

  1. Hirota, R., The direct method in soliton theory, Cambridge Tracts in Maohematics, Vol. 155, Cambridge University Press, Cambridge, 2004.

    Google Scholar 

  2. Hietarinta, J., Hirota’s bilinear method and soliton solutions, Phys. AUC, 15(1), 2005, 31–37.

    Google Scholar 

  3. 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.

    Article  Google Scholar 

  4. Ma, W. X. and Fan, E. G., Linear superposition principle applying to Hirota bilinear equations, Comput. Math. Appl., 61, 2011, 950–959.

    Article  MathSciNet  MATH  Google Scholar 

  5. 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.

    Article  MathSciNet  MATH  Google Scholar 

  6. Satsuma, J., A Wronskian representation of N-soliton solutions of nonlinear evolution equations, J. Phys. Soc. Jpn., 46, 1979, 359–360.

    Article  Google Scholar 

  7. Matveev, V. B., Positon-positon and soliton-positon collisions: KdV case, Phys. Lett. A, 166, 1992, 200–212.

    Google Scholar 

  8. Ma, W. X., Complexiton solutions to the Korteweg-de Vries equation, Phys. Lett. A, 301, 2002, 35–44.

    Article  MathSciNet  MATH  Google Scholar 

  9. Ma, W. X. and Maruno, K., Complexiton solutions of the Toda lattice equation, Physica A, 343, 2004, 219–237.

    MathSciNet  Google Scholar 

  10. Ma, W. X., Soliton, positon and negaton solutions to a Schrödinger self-consistent source equation, J. Phys. Soc. Jpn., 72, 2003, 3017–3019.

    Article  MATH  Google Scholar 

  11. Ma, W. X., Complexiton solutions of the Korteweg-de Vries equation with self-consistent sources, Chaos, Solitons Fractals, 26, 2005, 1453–1458.

    Article  MATH  Google Scholar 

  12. Nakamura, A., A bilinear N-soliton formula for the KP equation, J. Phys. Soc. Jpn., 58, 1989, 412–422.

    Article  Google Scholar 

  13. Hirota, R., Soliton solutions to the BKP equations — I. The Pfaffian technique, J. Phys. Soc. Jpn., 58, 1989, 2285–2296.

    Article  MathSciNet  Google Scholar 

  14. 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.

    Article  MathSciNet  MATH  Google Scholar 

  15. Wazwaz, A. M., Multiple-soliton solutions for a (3+1)-dimensional generalized KP equation, Commun. Nonlinear Sci. Numer. Simu., 17, 2012, 491–495.

    Article  MathSciNet  MATH  Google Scholar 

  16. 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.

    Article  Google Scholar 

  17. Ma, W. X. and Pekcan, A., Uniqueness of the Kadomtsev-Petviashvili and Boussinesq equations, Z. Naturforsch. A., 66, 2011, 377–382.

    Article  Google Scholar 

  18. 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.

    Article  MathSciNet  MATH  Google Scholar 

  19. Hirota, R., A new form of Bäcklund transformations and its relation to the inverse scattering problem, Progr. Theoret. Phys., 52, 1974, 1498–1512.

    Article  MATH  Google Scholar 

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Correspondence to Alrazi Abdeljabbar.

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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).

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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

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  • DOI: https://doi.org/10.1007/s11401-012-0738-8

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