Bilinear equations, Bell polynomials and linear superposition principle
By Wenxiu Ma. 2013
251 citations recorded by the source corpus.
A class of bilinear differential operators is introduced through assigning appropriate signs and used to create bilinear differential equations which generalize Hirota bilinear equations. The resulting bilinear differential equations are characterized by a special kind of Bell polynomials and the linear superposition principle is applied to the construction of their linear subspaces of solutions. Illustrative examples are made by an algorithm using weights of dependent variables.
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Citations in the corpus
- Constructing lump solutions to a generalized Kadomtsev–Petviashvili–Boussinesq equation (2016, background): “Note here that seven parameters c1, c2, a2, a3, a4, a6 and a8 are involved in the solution u(II), and they are demanded to satisfy conditions (22), (23) and (24) to guarantee u(II) to be lump solutions.”
- N-soliton solutions and the Hirota conditions in (2+1)-dimensions (2020, background): “A generalized bilinear equation possesses a resonant N-soliton solution (Ma 2013a, b): where ci ’s are arbitrary constants and i ’s are defined as in Sect.”