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A Partial Differential Equation Arising in a 1D Model for the 3D Vorticity Equation
Author(s) -
De Gregorio Salvatore
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199610)19:15<1233::aid-mma828>3.0.co;2-w
Subject(s) - first order partial differential equation , mathematics , burgers' equation , partial differential equation , korteweg–de vries equation , vorticity equation , fisher's equation , vorticity , generalization , differential equation , kadomtsev–petviashvili equation , universal differential equation , mathematical analysis , connection (principal bundle) , soliton , integro differential equation , exact differential equation , mathematical physics , vortex , physics , nonlinear system , geometry , quantum mechanics , thermodynamics
We continue the study of the one‐dimensional model for the vorticity equation considered in [4]. The partial differential equation σ yt +σσ xy =σ x σ y +νσ yxx is deduced, which appears as a generalization of the Burgers' equation, with possibly some connection also to the KdV equation. Some properties of this equation are given and propagating solutions are found which are of soliton type, both with non‐compact and compact support.