Journal
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
Volume 22, Issue 1, Pages -Publisher
SPRINGER BASEL AG
DOI: 10.1007/s12346-022-00684-w
Keywords
Shallow water; Nonlinear and dispersive long gravity waves; (2+1)-dimensional generalized modified dispersive water-wave system; Symbolic computation; Scaling transformation; Hetero-Backlund transformations; Similarity reductions
Categories
Ask authors/readers for more resources
This study conducts symbolic computation to analyze the nonlinear and dispersive long gravity waves propagating along two horizontal directions. It explores scaling transformations, hetero-Backlund transformations, and similarity reductions in the system, emphasizing the dependence on coefficients.
For the water waves, people consider some dispersive systems. Describing the nonlinear and dispersive long gravity waves travelling along two horizontal directions in the shallow water of uniform depth, we now symbolically compute a (2+1)-dimensional generalized modified dispersive water-wave system. With respect to the height of the water surface and horizontal velocity of the water wave, with symbolic computation, we work out (1) a set of the scaling transformations, (2) a set of the hetero-Backlund transformations, from that system to a known linear partial differential equation, and (3) four sets of the similarity reductions, each of which is from that system to a known ordinary differential equation. We pay attention that our hetero-Backlund transformations and similarity reductions rely on the coefficients in that system.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available