Transformations between Nonlocal and Local Integrable Equations
By Bo Yang, Jianke Yang. 2017
168 citations recorded by the source corpus.
Recently, a number of nonlocal integrable equations, such as the PT ‐symmetric nonlinear Schrödinger (NLS) equation and PT ‐symmetric Davey–Stewartson equations, were proposed and studied. Here, we show that many of such nonlocal integrable equations can be converted to local integrable equations through simple variable transformations. Examples include these nonlocal NLS and Davey–Stewartson equations, a nonlocal derivative NLS equation, the reverse space‐time complex‐modified Korteweg–de Vries (CMKdV) equation, and many others. These transformations not only establish immediately the integrability of these nonlocal equations, but also allow us to construct their Lax pairs and analytical solutions from those of the local equations. These transformations can also be used to derive new nonlocal integrable equations. As applications of these transformations, we use them to derive rogue wave solutions for the partially PT ‐symmetric Davey–Stewartson equations and the nonlocal derivative NLS equation. In addition, we use them to derive multisoliton and quasi‐periodic solutions in the reverse space‐time CMKdV equation. Furthermore, we use them to construct many new nonlocal integrable equations such as nonlocal short pulse equations, nonlocal nonlinear diffusion equations, and nonlocal Sasa–Satsuma equations.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/6af261927c744e59d78691142738279ede197c4d
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy (2018, methodology): “With the above mechanism, all the transformations between local equations and their nonlocal counterparts given in [42] are meaningful and practical.”