Bilinear Equations and Resonant Solutions Characterized by Bell Polynomials
By Wenxiu Ma. 2013
165 citations recorded by the source corpus.
Subfields: Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/9799a014b7ca04a80176ae99b7acc2c8b71332f2
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Citations in the corpus
- Lump and lump-soliton solutions to the $$(2+1)$$(2+1)-dimensional Ito equation (2018, background): “This kind of mixed solutions is different from resonant solutions by the linear superposition principle [35,36] and could describe complicated nonlinear physical phenomena.”
- Diversity of interaction solutions to the (2+1)-dimensional Ito equation (2017, background): “This kind of interaction solutions is quite different from resonant solutions formulated by the linear superposition principle [31,32] and could bring insights to help solve nonlinear problems we face today.”
- Abundant Mixed Lump-Soliton Solutions to the BKP Equation (2018, background): “Combination solutions of generalized bilinear and tri-linear differential equations with generalized bilinear derivatives [26] are also of interest, since the corresponding mixed interaction solutions are different from the resonant ones generated via linear superposition principle [27,28].”
- Lump and Interaction Solutions of Linear PDEs in (3 + 1)-Dimensions (2019, background): “Lumps and interaction solutions of generalised bilinear and tri-linear equations involving generalised bilinear derivatives [17, 18] are also interesting, and the corresponding interaction solutions will not be the resonant solutions obtained by the linear superposition principles in [19,20].”
- 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.”
- Abundant lumps and their interaction solutions of (3+1)-dimensional linear PDEs (2018, background): “resonant solutions generated through the linear superposition principle [40,41].”