Exact rational solutions to a Boussinesq-like equation in (1+1)-dimensions

Autor:	Bao-Zhu Zhao, Wen-Xiu Ma, Chang-Guang Shi
Rok vydání:	2015
Předmět:	Discrete mathematics Polynomial Pure mathematics Class (set theory) Nonlinear Sciences::Exactly Solvable and Integrable Systems Conjecture Zero of a function Degree (graph theory) Differential equation Applied Mathematics Bilinear interpolation Nonlinear differential equations Mathematics
Zdroj:	Applied Mathematics Letters. 48:170-176
ISSN:	0893-9659
Popis:	A Boussinesq-like nonlinear differential equation in ( 1 + 1 )-dimensions is introduced by using a generalized bilinear differential equation with the generalized bilinear derivatives D 3 , x and D 3 , t . A class of rational solutions, generated from polynomial solutions to the associated generalized bilinear equation, is constructed for the presented Boussinesq-like equation. It is conjectured that this class of rational solutions contain all such rational solutions to the new Boussinesq-like equation. More concretely, the conjecture says that if a polynomial f = f ( x , t ) in x and t solves f t t f − f t 2 + 3 f x x 2 = 0 , then the degree of f with respect to t must be less than or equal to 1.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::80a99c5fb1ca7420a6ee3a46b95bb4f6 https://doi.org/10.1016/j.aml.2015.04.002 Zobrazit plný text záznamu Full Text from ScienceDirect