Nonlinear Dynamics

, Volume 70, Issue 1, pp 189–196

# Localized coherent structures based on variable separation solution of the (2+1)-dimensional Boiti–Leon–Pempinelli equation

Original Paper

## Abstract

A new mapping equation (coupled Riccati equations) method is used to obtain three kinds of variable separation solutions with two arbitrary functions of the (2+1)-dimensional Boiti–Leon–Pempinelli equation. Based on the variable separation solution and by selecting appropriate functions, two type of multidromion excitations, that is, dromion lattice and multidromion solitoffs, are investigated. Moreover, we can discuss head-on collision and “chase and collision” phenomena between two multidromions.

## Keywords

Coupled Riccati equations method Boiti–Leon–Pempinelli equation Variable separation solutions Multidromions

## Notes

### Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11005092), the Program for Innovative Research Team of Young Teachers in Zhejiang A&F University (Grant No. 2009RC01), and the Scientific Research and Developed Fund of Zhejiang A&F University (Grant No. 2009FK42).

## References

1. 1.
Biswas, A., Khalique, C.M.: Stationary solutions for nonlinear dispersive Schrodinger’s equation. Nonlinear Dyn. 63, 623–626 (2011)
2. 2.
Zhang, Y., Yang, S., Li, C., Ge, J.Y., Wei, W.W.: Exact solutions and Painleve analysis of a new (2+1)-dimensional generalized KdV equation. Nonlinear Dyn. (2011). doi: Google Scholar
3. 3.
Zhang, S.: Exact solutions of a KdV equation with variable coefficients via Exp-function method. Nonlinear Dyn. 53, 11–17 (2008)
4. 4.
Ye, C.E., Zhang, W.G.: New explicit solutions for (2+1)-dimensional soliton equation. Chaos Solitons Fractals 44, 1063–1069 (2011)
5. 5.
Lü, X., Tian, B., Zhang, H.Q., Xu, T., Li, H.: Generalized (2+1)-dimensional Gardner model: bilinear equations, Backlund transformation, lax representation and interaction mechanisms. Nonlinear Dyn. 67, 2279–2290 (2012)
6. 6.
Lou, S.Y., Lu, J.Z.: Special solutions from variable separation approach: Davey–Stewartson equation. J. Phys. A, Math. Gen. 29, 4029–4215 (1996)
7. 7.
Tang, X.Y., Lou, S.Y., Zhang, Y.: Localized excitations in (2+1)-dimensional systems. Phys. Rev. E 66, 046601 (2002)
8. 8.
Ma, S.H., Zhang, Y.L.: Fractal structures and chaotic behaviors in a (2+1)-dimensional nonlinear system. Commun. Theor. Phys. 57, 1117–1121 (2010) Google Scholar
9. 9.
Zheng, C.L., Fang, J.P., Chen, L.Q.: New variable separation excitations of a (2+1)-dimensional Broer–Kaup–Kupershmidt system obtained by an extended mapping approach. Z. Naturforsch. A 59, 912–918 (2004) Google Scholar
10. 10.
Dai, C.Q., Zhou, G.Q.: Exotic interactions between solitons of the (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov system. Chin. Phys. 16, 1201–1208 (2007).
11. 11.
Dai, C.Q., Zhou, G.Q., Zhang, J.F.: Exotic localized structures based on variable separation solution of (2+1)-dimensional KdV equation via the extended tanh-function method. Chaos Solitons Fractals 33, 1458–1467 (2007).
12. 12.
Yang, Z., Ma, S.H., Fang, J.P.: Chaotic solutions of (2+1)-dimensional Broek–Kaup equation with variable coefficients. Chin. Phys. B 20, 040301 (2011)
13. 13.
Dai, C.Q., Zhang, J.F.: New types of interactions based on variable separation solutions via the general projective Riccati equation method. Rev. Math. Phys. 19, 195–221 (2007)
14. 14.
Dai, C.Q.: Semifoldons with fusion and fision properties of (2+1)-dimensional nonlinear system. Chaos Solitons Fractals 38, 474–480 (2008)
15. 15.
Boiti, M., Leon, J.J.P., Pempinelli, F.: Spectral transform for a two spatial dimension extension of the dispersive long wave equation. Inverse Probl. 3, 371–387 (1987)
16. 16.
Garagash, T.I.: Modification of the Painleve test for systems of nonlinear partial differential equations. Theor. Math. Phys. 100, 1075–1081 (1994)
17. 17.
Lu, Z.S., Zhang, H.Q.: Soliton like and multi-soliton like solutions for the Boiti–Leon–Pempinelli equation. Chaos Solitons Fractals 19, 527–531 (2004)
18. 18.
Dai, C.Q., Wang, Y.Y.: Periodic structures based on variable separation solution of the (2+1)-dimensional Boiti–Leon–Pempinelli equation. Chaos Solitons Fractals 39, 350–355 (2009)
19. 19.
Ma, S.H., Zhang, Y.L.: Fractal structures and chaotic behaviors in a (2+1)-dimensional nonlinear system. Commun. Theor. Phys. 57, 1117–1121 (2010) Google Scholar
20. 20.
Dai, C.Q., Wang, Y.Y.: Combined wave solutions of the (2+1)-dimensional generalized Nizhnik–Novikov–Veselov system. Phys. Lett. A 372, 1810–1815 (2008)
21. 21.
Babaoglu, C.: Some special solutions of a generalized Davey–Stewartson system. Chaos Solitons Fractals 30, 781–790 (2006)
22. 22.
Ma, S.H., Fang, J.P.: New exact solutions and localized excitations in a (2+1)-dimensional soliton system. Z. Naturforsch. A 64, 37–43 (2009) Google Scholar
23. 23.
Zheng, C.L., Fang, J.P., Chen, L.Q.: Soliton fission and fusion in (2+1)-Dimensional Boiti–Leon–Pempinelli system. Commun. Theor. Phys. 43, 681–687 (2005)