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General breather solution to the Sasa–Satsuma equation (SSE) is systematically investigated in this paper. We firstly transform the SSE into a set of three Hirota bilinear equations under a proper plane wave boundary condition. Starting from a specially arranged tau-function of the Kadomtsev–Petviashvili hierarchy and a set of 11 bilinear equations satisfied, we implement a series steps of reduction procedure, i.e. C-type reduction, dimension reduction and complex conjugate reduction, and reduce these 11 equations to three bilinear equations for the SSE. Meanwhile, the general breather solution to the SSE is found in determinant of even order. The one- and two-breather solutions are calculated and analysed in detail.
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An integrable semidiscretization of the modified Camassa–Holm equation with linear dispersion term
Abstract In the present paper, we are with integrable discretization of a modified Camassa–Holm (mCH) equation with linear dispersion term. The key of the construction is the semidiscrete analog for a set of bilinear equations of the mCH equation. First, we show that these bilinear equations and their determinant solutions either in Gram‐type or Casorati‐type can be reduced from the discrete Kadomtsev–Petviashvili (KP) equation through Miwa transformation. Then, by scrutinizing the reduction process, we obtain a set of semidiscrete bilinear equations and their general soliton solution in Gram‐type or Casorati‐type determinant form. Finally, by defining dependent variables and discrete hodograph transformations, we are able to derive an integrable semidiscrete analog of the mCH equation. It is also shown that the semidiscrete mCH equation converges to the continuous one in the continuum limit.
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- Award ID(s):
- 1715991
- PAR ID:
- 10445423
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Studies in Applied Mathematics
- Volume:
- 149
- Issue:
- 1
- ISSN:
- 0022-2526
- Page Range / eLocation ID:
- p. 230-265
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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