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Complexiton solutions of the Toda lattice equation

Author

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  • Ma, Wen-Xiu
  • Maruno, Ken-ichi

Abstract

A set of coupled conditions consisting of differential-difference equations is presented for Casorati determinants to solve the Toda lattice equation. One class of the resulting conditions leads to an approach for constructing complexiton solutions to the Toda lattice equation through the Casoratian formulation. An analysis is made for solving the resulting system of differential-difference equations, thereby providing the general solution yielding eigenfunctions required for forming complexitons. Moreover, a feasible way is presented to compute the required eigenfunctions, along with examples of real complexitons of lower order.

Suggested Citation

  • Ma, Wen-Xiu & Maruno, Ken-ichi, 2004. "Complexiton solutions of the Toda lattice equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 219-237.
    • Handle: RePEc:eee:phsmap:v:343:y:2004:i:c:p:219-237
    DOI: 10.1016/j.physa.2004.06.072
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    Citations

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    Cited by:

    1. Ma, Wen-Xiu, 2005. "Complexiton solutions of the Korteweg–de Vries equation with self-consistent sources," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1453-1458.
    2. Xu, Xi-Xiang, 2015. "A deformed reduced semi-discrete Kaup–Newell equation, the related integrable family and Darboux transformation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 275-283.
    3. Xia, Yonghui & Han, Maoan, 2009. "Multiple periodic solutions of a ratio-dependent predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1100-1108.
    4. Yu, Guo-Fu & Hu, Xing-Biao, 2009. "Extended Gram-type determinant solutions to the Kadomtsev–Petviashvili equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 184-191.
    5. Seadawy, A.R. & El-Kalaawy, O.H. & Aldenari, R.B., 2016. "Water wave solutions of Zufiria’s higher-order Boussinesq type equations and its stability," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 57-71.

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