scholarly journals Quasi-periodic solutions of beam equations with the nonlinear terms depending on the time and space variables

2016 ◽  
Vol 47 (2) ◽  
pp. 257-290
Author(s):  
SI JianGuo ◽  
WANG Yi
Keyword(s):  
Periodic Solutions ◽  
Time And Space ◽  
Beam Equations

Multiple doubly periodic solutions of semi-linear damped beam equations

2007 ◽  
Vol 67 (5) ◽  
pp. 1540-1549
Author(s):  
Peng Wang ◽  
Yukun An
Keyword(s):  
Periodic Solutions ◽  
Beam Equations

scholarly journals Multiple-soliton and Periodic Solutions to Space-time Fractional Whitham-Broer-Kaup Equations

2021 ◽  
Author(s):  
Hang Xu ◽  
Jifeng Cui
Keyword(s):  
Nonlinear System ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Fractional Order ◽  
Space Time ◽  
Wave System ◽  
Time And Space ◽  
Solitary Solutions ◽  
Nonlinear Wave System

Abstract In this paper, the space-time fractional Whitham-Broer-Kaup equations are investigated. By means of new fractional scaling transformations, the fractional nonlinear system of different time and space orders is transformed to the integer one. The multiple solitary solutions and periodic solutions are obtained respectively. All those solutions are given exactly by introducing new scaling transformations, which makes our study is unique and different from most existing studies. It is expected that exact solutions for nonlinear wave system of fractional order can be handled in the similar way.

scholarly journals Almost-Periodic Response Solutions for a Forced Quasi-Linear Airy Equation

2020 ◽  
Author(s):  
Livia Corsi ◽  
Riccardo Montalto ◽  
Michela Procesi
Keyword(s):  
Periodic Solutions ◽  
Differential Calculus ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Time And Space ◽  
Periodic Response ◽  
Linear Pde ◽  
Linear Perturbations ◽  
Airy Equation

Abstract We prove the existence of almost-periodic solutions for quasi-linear perturbations of the Airy equation. This is the first result about the existence of this type of solutions for a quasi-linear PDE. The solutions turn out to be analytic in time and space. To prove our result we use a Craig–Wayne approach combined with a KAM reducibility scheme and pseudo-differential calculus on $$\mathbb {T}^\infty $$ T ∞ .

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