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Localized coherent structures of the (2+1)-dimensional higher order Broer-Kaup equations

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Abstract

By using the extended homogeneous balance method, the localized coherent structures are studied. A nonlinear transformation was first established, and then the linearization form was obtained based on the extended homogenous balance method for the higher order (2+1)-dimensional Broer-Kaup equations. Starting from this linearization form equation, a variable separation solution with the entrance of some arbitrary functions and some arbitrary parameters was constructed. The quire rich localized coherent structures were revealed. This method, which can be generalized to other (2+1)-dimensional nonlinear evolution equation, is simple and powerful.

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References

  1. Boiti M, Leon J J P, Martina L, et al. Scattering of localized solitions in the plane[J].Phys Lett A, 1988,132(8–9):432–439.

    Article  MathSciNet  Google Scholar 

  2. Fokas A S, Santini P M. On the simplest integrable equation in 2+1[J].Physica D, 1990,44 (1):99–104; Hietarinta J, Hirota R. Multidromion solutions to the Davey-stewartson equation [J].Phys Lett A, 1990,145(5):237–244.

    Article  MathSciNet  Google Scholar 

  3. Hietarinta J. One-dromion solutions for generic classes of equations[J].Phys Lett A, 1990,149 (2–3):113–117.

    Article  MathSciNet  Google Scholar 

  4. Radha R, Lakshmanan M. Singularity analysis and localized coheren structures in (2+1)-dimensional generalized Korteweg-de Vries equations[J].J Math Phys, 1994,35(9):4746–4756.

    Article  MathSciNet  MATH  Google Scholar 

  5. Radha R, Lakshmanan M. Dromion like structures in the (2+1)-dimensional breaking soliton equation[J].Phys Lett A, 1995,197(1):7–12.

    Article  MathSciNet  MATH  Google Scholar 

  6. Radha R, Lakshmanan M. Exotic coherent structures in the (2+1)-dimensional long dispersive wave equation[J].J Math Phys, 1997,38(2):292–299.

    Article  MathSciNet  MATH  Google Scholar 

  7. Radha R, Lakshmanan M. A new class of induced localized structures in the (2+1)-dimensional scalar nonlinear Schrödinger equations[J].J Phys A, 1997,30:3229–3232.

    Article  MathSciNet  MATH  Google Scholar 

  8. Lou S Y, Dromion-like structures in a (3+1)-dimensional KdV-type equation[J].J Phys A, 1996,29:5989–6001.

    Article  MathSciNet  MATH  Google Scholar 

  9. Ruan H Y, Lou S Y. Higher-dimensional dromion structures: Jimbo-Miwa-kadomtsev-Petviashvili system[J].J Math Phys, 1997,38(6):3123–3136.

    Article  MathSciNet  MATH  Google Scholar 

  10. Lou S Y. Generalized dromion solutions of the (2+1)-dimensional KdV equation[J].J Phys A, 1995,28:7227–7232.

    Article  MathSciNet  MATH  Google Scholar 

  11. Lou S Y. On the dromion solutions of the potential breaking soliton equation[J].Commun Theor, 1996,26(4):487–492.

    Google Scholar 

  12. Radha R, Lakshmanan M. Generalized dromions in the (2+1)-dimensional long dispersive wave (2LDW) and scalar nonlinear Schrödinger(NLS) equations[J].Chaos Solitons & Fractals, 1999,10:1821–1824.

    Article  MathSciNet  MATH  Google Scholar 

  13. ZHANG Jie-fang. Generalized dromions of the (2+1)-dimensional nonlinear Schrödinger equations [J].Communcation in Nonlinear Science & Numerical Simulation, 2001,6(1):50–53.

    Article  Google Scholar 

  14. ZHANG Jie-fang. A simple soliton solution method for the (2+1)-dimensional long dispersive wave equations[J].Acta Physica Sinica (Overseas Edition), 1999,8(2):326–330.

    Article  Google Scholar 

  15. Lou S Y. On the coherent structures of the Nizhnik-Novikov-Veselov equation[J].Phys Lett A, 2000,277:94–100.

    Article  MathSciNet  MATH  Google Scholar 

  16. Lou S Y, Ruan H Y. Revisitation of the localized excitations of the (2+1)-dimensional KdV equation[J].J Phys A: Math Gen, 2001,34:305–316.

    Article  MathSciNet  MATH  Google Scholar 

  17. RUAN Hang-yu, CHEN Yi-xin. Ring solitons, dromions, breathers and instantons of the NLS equation[J].Acta Physica Sinica, 2001,50(4):586–591.

    MathSciNet  MATH  Google Scholar 

  18. WANG Ming-liang. The solitary wave solutions for variant Boussinesq equations[J].Phys Lett A, 1995,199:169–172.

    Article  MathSciNet  Google Scholar 

  19. ZHANG Jie-fang. Multiple soliton solutions for the approximate equation of long wave water[J].Acta Physica Sinica, 1998,47(9):1416–1420; Multi-soliton solutions of the dispersive long wave equation[J].Chin Phys Lett, 1999,16(1):659–661.

    MathSciNet  MATH  Google Scholar 

  20. ZHANG Jie-fang. Bäcklund transformation and multisoliton-like solution of the (2+1)-dimensional dispersive long wave equations[J].Commun Theor Phys, 2000,33(4):577–582.

    MathSciNet  Google Scholar 

  21. FANG Een-gui, ZHANG Hong-qing. Solitary wave solution of nonlinear wave equation[J].Acta Physica Sinica, 1997,46(1):1254–1259.

    MathSciNet  Google Scholar 

  22. LOU Sen-yue, WU Xing-biao. Broer-Kaup systems from Darboux transformation related symmetry constraints of KP equation[J].Commun Theor Phys, 1998,29(1):145–148.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai, P R China

    Zhang Jie-fang & Liu Yu-lu

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  1. Zhang Jie-fang
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  2. Liu Yu-lu
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Contributed by LIU Yu-lu

Foundation item: the National Natural Science Foundation of China (19872043)

Biographies: ZHANG Jie-fang (1959-), Professor; LIU Yu-lu (1959-), Professor, Ph Doctor

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Jie-fang, Z., Yu-lu, L. Localized coherent structures of the (2+1)-dimensional higher order Broer-Kaup equations. Appl Math Mech 23, 549–556 (2002). https://doi.org/10.1007/BF02437773

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  • DOI: https://doi.org/10.1007/BF02437773

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