Multisoliton solutions of the two-component Camassa-Holm equation and its reductions. (English. Russian original) Zbl 1516.35362
Theor. Math. Phys. 214, No. 3, 308-333 (2023); translation from Teor. Mat. Fiz. 214, No. 3, 359-386 (2023).
Summary: The Bäcklund transformation for an integrable two-component Camassa-Holm (2CH) equation is presented and studied. It involves both dependent and independent variables. A nonlinear superposition formula is given for constructing multisoliton, multiloop, and multikink solutions of the 2CH equation. We also present solutions of the Camassa-Holm equation, the two-component Hunter-Saxton (2HS) equation, and the Hunter-Saxton equation, which all arise from solutions of the 2CH equation. By appropriate limit procedures, a solution of the 2HS equation is successfully obtained from that of the 2CH equation, which is worked out with the method of Bäcklund transformations. By analyzing the solution, we obtain the soliton and loop solutions for 2HS equation.
MSC:
| 35Q51 | Soliton equations |
| 35C08 | Soliton solutions |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
Keywords:
two-component Camassa-Holm equation; two-component Hunter-Saxton equation; Bäcklund transformation; soliton; reductionReferences:
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