Open AccessApplication of the bifurcation method to the modified Boussinesq equation
Author(s) -
Shaoyong Li
Publication year - 2014
Publication title -
electronic journal of qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2014.1.42
Subject(s) - mathematics , bifurcation , boussinesq approximation (buoyancy) , mathematical analysis , calculus (dental) , mechanics , nonlinear system , physics , heat transfer , medicine , quantum mechanics , natural convection , dentistry , rayleigh number
In this paper, we investigate the modified Boussinesq equation utt − uxx − euxxxx − 3(u)xx + 3(uux)x = 0. Firstly, we give a property of the solutions of the equation, that is, if 1+ u(x, t) is a solution, so is 1− u(x, t). Secondly, by using the bifurcation method of dynamical systems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom