Nonlocal Symmetries, Conservation Laws and Interaction Solutions of the Generalised Dispersive Modified Benjamin–Bona–Mahony Equation

Autor:	Min-Jie Dong, Tian-Tian Zhang, Shou-Fu Tian, Xue-Wei Yan, Xiu-Bin Wang
Rok vydání:	2018
Předmět:	Lie point symmetry Physics Conservation law Benjamin–Bona–Mahony equation 0103 physical sciences Homogeneous space General Physics and Astronomy Physical and Theoretical Chemistry 010306 general physics 01 natural sciences Mathematical Physics 010305 fluids & plasmas Mathematical physics
Zdroj:	Zeitschrift für Naturforschung A. 73:399-405
ISSN:	1865-7109 0932-0784
DOI:	10.1515/zna-2017-0436
Popis:	We consider the generalised dispersive modified Benjamin–Bona–Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.
Databáze:	OpenAIRE
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