Periodic solutions of an infinite dimensional riccati equation

1986 ◽  
pp. 714-722 ◽  
Author(s):  
G. Da Prato
Keyword(s):  
Periodic Solutions ◽  
Riccati Equation ◽  
Infinite Dimensional

Quasi-Periodic Solutions of Nonlinear Wave Equation with x-Dependent Coefficients

2015 ◽  
Vol 25 (03) ◽  
pp. 1550043 ◽  
Author(s):  
Yixian Gao ◽  
Weipeng Zhang ◽  
Shuguan Ji
Keyword(s):  
Wave Equation ◽  
Normal Form ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Seismic Waves ◽  
Birkhoff Normal Form ◽  
General Boundary Conditions ◽  
Kam Theorem ◽  
Infinite Dimensional

This paper is devoted to the study of quasi-periodic solutions of a nonlinear wave equation with x-dependent coefficients. Such a model arises from the forced vibration of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. Based on the partial Birkhoff normal form and an infinite-dimensional KAM theorem, we can obtain the existence of quasi-periodic solutions for this model under the general boundary conditions.

scholarly journals Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Alvaro H. Salas S ◽  
Cesar A. Gómez S
Keyword(s):  
Exact Solutions ◽  
Periodic Solutions ◽  
Riccati Equation ◽  
Function Method ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Third Order ◽  
Forcing Term ◽  
Projective Riccati Equation Method

The general projective Riccati equation method and the Exp-function method are used to construct generalized soliton solutions and periodic solutions to special KdV equation with variable coefficients and forcing term.

scholarly journals The new exact solitary solutions for the (3+1)-dimensional Zakharov-Kuznetsov equation using the Riccati equation

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 3995-4000
Author(s):  
Xiao-Jun Yin ◽  
Quan-Sheng Liu ◽  
Lian-Gui Yang ◽  
N Narenmandula
Keyword(s):  
Exact Solutions ◽  
Periodic Solutions ◽  
Riccati Equation ◽  
Electrostatic Potential ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
The Other ◽  
Equation Method ◽  
Wave Solutions ◽  
Solitary Solutions

In this paper, a non-linear (3+1)-dimensional Zakharov-Kuznetsov equation is investigated by employing the subsidiary equation method, which arises in quantum magneto plasma. The periodic solutions, rational wave solutions, soliton solutions for the quantum Zakharov-Kuznetsov equation which play an important role in mathematical physics are obtained with the help of the Riccati equation expan?sion method. Meanwhile, the electrostatic potential can be accordingly obtained. Compared to the other methods, the exact solutions obtained will extend on earlier reports by using the Riccati equation.

Periodic solutions of the Riccati equation

1980 ◽  
Author(s):  
Robert Hermann ◽  
Clyde Martin
Keyword(s):  
Periodic Solutions ◽  
Riccati Equation
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