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Title: 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
NSF-PAR ID:
10445423
Author(s) / Creator(s):
 ;  ;  
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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