Complexiton solutions of the Toda lattice equation

By Wenxiu Ma, Ken-ichi Maruno. 2004

149 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/95ca89b7306b014e39d16a88eeda246119eda2b3

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In Geometry and Topology

1. Wenxiu Ma
2. Jingsong He
3. Chunxia Li
4. Yuncheng You
5. Yufeng Zhang
6. Xi-Xiang Xu
7. Jin-Yun Yang
8. Ma Wen-Xiu

In Statistical and Nonlinear Physics

1. Wenxiu Ma
2. Xi-Xiang Xu
3. Yufeng Zhang
4. Jingsong He
5. Chunxia Li
6. Yuncheng You
7. Jin-Yun Yang
8. Ma Wen-Xiu

Citations in the corpus

• A second Wronskian formulation of the Boussinesq equation (2009, background): “In addition to rational solutions, positons and complexitons to the Boussinesq equation I, one can also construct interaction solutions between any two different kinds of solutionswithin the establishedWronskian formulation (see [32,4] for the cases of the KdV equation and the Toda lattice equation)”
• Semidirect sums of Lie algebras and discrete integrable couplings (2006, background): “There exist a voluminous literature on the Toda lattice equation, and its generalizations and solution structures (for example, see [27]-[32]).”
• Riemann–Hilbert problems andN-soliton solutions for a coupled mKdV system (2018, background): “How about other solutions such as positon solutions and complexiton solutions [25,26]? About systems of coupled mKdV equations, there are other studies such as integrable couplings [27], super hierarchies [28] and fractional counterparts [29].”
• Semi-direct sums of Lie algebras and continuous integrable couplings (2006, background): “) is linearly independent of the Toda lattice equation (3.10). There exist a voluminous literature on the Toda lattice equation, and its generalizations and solution structures (for example, see [27]-[32]). 3.2 Integrable couplings from specific semi-direct sums The generalized Toda spectral problem ”
• Rational solutions of the Toda lattice equation in Casoratian form (2004, background): “The case of complex eigenvalues corresponds to complexitons [16].”