scholarly journals Blow-up phenomena for the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jinxing Liu ◽  
Xiongrui Wang ◽  
Jun Zhou ◽  
Huan Zhang
Keyword(s):  
Lower Bounds ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
Blow Up ◽  
Sixth Order ◽  
Upper And Lower Bounds ◽  
Differential Inequalities ◽  
Nonlinear Source ◽  
Order Dispersion ◽  
Dispersion Term

<p style='text-indent:20px;'>This paper deals with the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source. By using some ordinary differential inequalities, the conditions on finite time blow-up of solutions are given with suitable assumptions on initial values. Moreover, the upper and lower bounds of the blow-up time are also investigated.</p>

Global existence and blow-up for the generalized sixth-order Boussinesq equation

2012 ◽  
Vol 75 (11) ◽  
pp. 4325-4338 ◽  
Author(s):  
Amin Esfahani ◽  
Luiz Gustavo Farah ◽  
Hongwei Wang
Keyword(s):  
Global Existence ◽  
Boussinesq Equation ◽  
Blow Up ◽  
Sixth Order

scholarly journals Construction of Analytic Solution for Time-Fractional Boussinesq Equation Using Iterative Method

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Fei Xu ◽  
Yixian Gao ◽  
Weipeng Zhang
Keyword(s):  
Analytical Solution ◽  
Iterative Method ◽  
Fourth Order ◽  
Iterative Process ◽  
Boussinesq Equation ◽  
Analytic Solution ◽  
Boussinesq Equations ◽  
Sixth Order ◽  
Linear And Nonlinear

This paper is aimed at constructing analytical solution for both linear and nonlinear time-fractional Boussinesq equations by an iterative method. By the iterative process, we can obtain the analytic solution of the fourth-order time-fractional Boussinesq equation inR,R2, andRn, the sixth-order time-fractional Boussinesq equation, and the2nth-order time-fractional Boussinesq equation inR. Through these examples, it shows that the method is simple and effective.

scholarly journals Blow-up for the sixth-order multidimensional generalized Boussinesq equation with arbitrarily high initial energy

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jianghao Hao ◽  
Aiyuan Gao
Keyword(s):  
Cauchy Problem ◽  
Fourier Transform ◽  
Finite Time ◽  
Boussinesq Equation ◽  
Blow Up ◽  
Initial Energy ◽  
Sixth Order ◽  
The Cauchy Problem ◽  
Generalized Boussinesq Equation

AbstractIn this paper, we consider the Cauchy problem for the sixth-order multidimensional generalized Boussinesq equation with double damping terms. By using the improved convexity method combined with Fourier transform, we show the finite time blow-up of solution with arbitrarily high initial energy.

scholarly journals Dynamic Behaviors of Soliton Solutions for a Three-Coupled Lakshmanan-Porsezian-Daniel Model

2021 ◽  
Author(s):  
Beibei Hu ◽  
Ji Lin ◽  
Ling Zhang
Keyword(s):  
Spectral Analysis ◽  
Fourth Order ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Nonlinear Dynamical ◽  
Jump Matrix ◽  
Dynamical Behaviors ◽  
Helical Protein ◽  
Order Dispersion ◽  
Dispersion Term

Abstract In this paper, we use the Riemann-Hilbert (RH) approach to examine the integrable three-coupled Lakshmanan-Porsezian-Daniel (LPD) model, which describe the dynamics of alpha helical protein with the interspine coupling at the fourth-order dispersion term. Through the spectral analysis of Lax pair, we construct the higher order matrix RH problem for the three-coupled LPD model, when the jump matrix of this particular RH problem is a 4×4 unit matrix, the exact N-soliton solutions of the three-coupled LPD model can be exhibited. As special examples, we also investigate the nonlinear dynamical behaviors of the single-soliton, two-soliton, three-soliton and breather soliton solutions. Finally, an integrable generalized N-component LPD model with its linear spectral problem is discussed.

scholarly journals SOME COMPACTNESS RESULTS RELATED TO SCALAR CURVATURE DEFORMATION

2007 ◽  
Vol 09 (01) ◽  
pp. 81-120 ◽  
Author(s):  
YU YAN
Keyword(s):  
Scalar Curvature ◽  
Lower Bounds ◽  
Blow Up ◽  
Upper And Lower Bounds ◽  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Locally Conformally Flat ◽  
Curvature Deformation ◽  
Flat Manifolds ◽  
Curvature Problem

Motivated by the prescribing scalar curvature problem, we study the equation [Formula: see text] on locally conformally flat manifolds (M,g) with R(g) ≡ 0. We prove that when K satisfies certain conditions and the dimension of M is 3 or 4, any positive solution u of this equation with bounded energy has uniform upper and lower bounds. Similar techniques can also be applied to prove that on four-dimensional locally conformally flat scalar positive manifolds the solutions of [Formula: see text] can only have simple blow-up points.

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