Moving breathers and breather-to-soliton conversions for the Hirota equation. (English) Zbl 1371.35270
Summary: We find that the Hirota equation admits breather-to-soliton conversion at special values of the solution eigenvalues. This occurs for the first-order, as well as higher orders, of breather solutions. An analytic expression for the condition of the transformation is given and several examples of transformations are presented. The values of these special eigenvalues depend on two free parameters that are present in the Hirota equation. We also find that higher order breathers generally have complicated quasi-periodic oscillations along the direction of propagation. Various breather solutions are considered, including the particular case of second-order breathers of the nonlinear Schrödinger equation.
MSC:
35Q55 | NLS equations (nonlinear Schrödinger equations) |
35A30 | Geometric theory, characteristics, transformations in context of PDEs |
35C08 | Soliton solutions |
35Q53 | KdV equations (Korteweg-de Vries equations) |
37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |