Residual symmetry analysis and CRE integrability of the (3 + 1) -dimensional Burgers system
Institute of Nonlinear Science, Shaoxing University, 312000, Shaoxing, China
2 Yuanpei College, Shaoxing University, 312000, Shaoxing, China
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Accepted: 7 October 2018
Published online: 10 December 2018
The residual symmetry of the (3 + 1) -dimensional Burgers system is localized to a Lie point symmetry in a prolonged system and the corresponding finite transformation is obtained by using Lie’s first theorem. By further localize the linear superposition of multiple residual symmetries, the N -th Bäcklund transformations (BT) of the (3 + 1) -dimensional Burgers system are also got. By applying the standard Lie symmetry method to the prolonged system, not only the Lie symmetry group but also the symmetry reduction solutions are obtained, which include abundant interaction solutions between solitons and nonlinear waves. Furthermore, the (3 + 1) -dimensional Burgers system is proved to have consistent Riccati expansion (CRE) property, based on which some new BTs are given.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018