scholarly journals Two Different Systematic Techniques to Seek Analytical Solutions of the Higher-Order Modified Boussinesq Equation

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 96818-96826 ◽  
Author(s):  
Yongyi Gu ◽  
Yinying Kong
Keyword(s):  
Analytical Solutions ◽  
Boussinesq Equation ◽  
Higher Order ◽  
Modified Boussinesq Equation

SPACE OF HIGHER ORDER DIFFERENTIAL OPERATORS ON S1 AND INTEGRABLE FLOWS

2005 ◽  
Vol 02 (04) ◽  
pp. 619-631 ◽  
Author(s):  
PARTHA GUHA
Keyword(s):  
Boussinesq Equation ◽  
Differential Operators ◽  
Kdv Equation ◽  
Type Systems ◽  
Higher Order ◽  
Projective Structure ◽  
Order Operator ◽  
Third Order ◽  
The Third ◽  
Modified Boussinesq Equation

We study the action of vector field Vect(S1) on the space of higher order differential operators [Formula: see text], and its connection to projective structure on S1. In particular, we study the Euler–Poincaré flows on the space of third order differential operators and its relation to Drienfeld–Sokolov and coupled KdV type systems. We also discuss the Boussinesq equation associated with the third order operator. We study the factorization of higher order operators and its compatibility with the action of Vect(S1). We obtain the generalized Miura transformation and its connection to the modified Boussinesq equation. Finally, we also discuss flows on the special higher order differential operators for all ui = f(u,ux,uxx…) and its connection to KdV equation.

Analytical Solutions to the Linearized Boussinesq Equation for Assessing the Effects of Recharge on Aquifer Discharge1

2010 ◽  
Vol 46 (6) ◽  
pp. 1116-1132 ◽  
Author(s):  
Kevin G. Boggs ◽  
Robert W. Van Kirk ◽  
Gary S. Johnson ◽  
Jerry P. Fairley ◽  
P. Steve Porter
Keyword(s):  
Analytical Solutions ◽  
Boussinesq Equation ◽  
Linearized Boussinesq Equation

On the quasi-periodic solutions for generalized Boussinesq equation with higher order nonlinearity

2014 ◽  
Vol 94 (10) ◽  
pp. 1977-1996 ◽  
Author(s):  
Yanling Shi ◽  
Junxiang Xu ◽  
Xindong Xu ◽  
Shunjun Jiang
Keyword(s):  
Periodic Solutions ◽  
Boussinesq Equation ◽  
Higher Order ◽  
Generalized Boussinesq Equation
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