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Consistent Riccati Expansion for Integrable Systems
Author(s) -
Lou S. Y.
Publication year - 2015
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12072
Subject(s) - integrable system , mathematics , riccati equation , mathematical physics , nonlinear system , transformation (genetics) , korteweg–de vries equation , soliton , periodic wave , symmetry (geometry) , mathematical analysis , traveling wave , partial differential equation , physics , quantum mechanics , geometry , biochemistry , chemistry , gene
A consistent Riccati expansion (CRE) is proposed for solving nonlinear systems with the help of a Riccati equation. A system having a CRE is then defined to be CRE solvable. The CRE solvability is demonstrated quite universal for various integrable systems including the Korteweg–de Vries, Kadomtsev–Petviashvili, Ablowitz–Kaup–Newell–Segur (and then nonlinear Schrödinger), sine‐Gordon, Sawada–Kotera, Kaup–Kupershmidt, modified asymmetric Nizhnik–Novikov–Veselov, Broer–Kaup, dispersive water wave, and Burgers systems. In addition, it is revealed that many CRE solvable systems share a similar determining equation describing the interactions between a soliton and a cnoidal wave. They have a common nonlocal symmetry expression and they possess a formally universal once Bäcklund transformation.