Solutions to the complex shifted reverse space-time modified Korteweg-de Vries equation. (English) Zbl 1518.83111
Summary: According to the new nonlocal integrable reduction proposed by Ablowitz and Musslimani, we study the complex shifted reverse space-time modified Korteweg-de Vries equation. The soliton, the kink-type breather and higher-order rogue waves solutions are constructed by using the Darboux transformation method. The effects of the spectral parameter and space-time shift parameters on the solution are discussed respectively, and the dynamic behavior of them is described from the expression and image of the solution. In addition, by comparing with the standard PT symmetry, we discuss the new structure of different solutions due to the space-time shift parameters.
MSC:
| 83F05 | Relativistic cosmology |
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
| 35Q05 | Euler-Poisson-Darboux equations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 70H33 | Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics |
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