The Residual Symmetry and Consistent Tanh Expansion for the Benney System
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Zheng-Yi Ma
,
Jin-Xi Fei
Abstract
The residual symmetry of the (2+1)-dimensional Benney system is derived from the truncated Painlevé expansion. Such residual symmetry is localised and the original Benney equation is extended into an enlarged system by introducing four new variables. By using Lies first theorem, we obtain the finite transformation for the localised residual symmetry. More importantly, we further localise the linear superposition of multiple residual symmetries and construct the nth Bäcklund transformation for the Benney system in the form of the determinant. Moreover, it is proved that the (2+1)-dimensional Benney system is consistent tanh expansion (CTE) solvable. The exact interaction solutions between solitons and any other types of potential Burgers waves are also obtained, which include soliton-error function waves, soliton-periodic waves, and so on.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 11447017), the Natural Science Foundation of Zhejiang Province (Grant No. LY14A010005), and the Scientific Research Foundation of the First-Class Discipline of Zhejiang Province (B) (No. 201601).
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©2017 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
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- The Residual Symmetry and Consistent Tanh Expansion for the Benney System
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Artikel in diesem Heft
- Frontmatter
- Explicit Solutions and Conservation Laws of a Coupled Burgers’ Equation
- Residual Symmetry Analysis for Novel Localized Excitations of a (2+1)-Dimensional General Korteweg-de Vries System
- Mechanical, Electronic, and Optical Properties of β-B6O: First-Principles Calculations
- On a Super Generalized X-Dependent Hirota Equation
- The Slug and Churn Turbulence Characteristics of Oil–Gas–Water Flows in a Vertical Small Pipe
- Flow and Heat Transfer in a Newtonian Nanoliquid due to a Curved Stretching Sheet
- The Pressure Dependence of Structural, Electronic, Mechanical, Vibrational, and Thermodynamic Properties of Palladium-Based Heusler Alloys
- Exact Analysis of the Flow and Heat Transfer of the SA-TiO2 Non-Newtonian Nanofluid Between Two Coaxial Cylinders Through a Porous Medium
- The Residual Symmetry and Consistent Tanh Expansion for the Benney System
- On the Shallow Water Equations
- Letter
- Zero-Time Tunneling – Revisited
