A “direct” method to prove the generalized Itô–Venttsel’ formula for a generalized stochastic differential equation

2016 ◽  
Vol 26 (1) ◽  
pp. 17-29 ◽  
Author(s):  
E. V. Karachanskaya
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Direct Method ◽  
A Direct Method

To Investigate the Euler Solution of Differential Equation

2014 ◽  
Vol 614 ◽  
pp. 409-412
Author(s):  
Lin Long Zhao
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Euler Equations ◽  
Direct Method ◽  
Special Solution ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Euler Solution ◽  
A Direct Method

For Euler Equations L(y）=∑aixiy(i) =f(x)are Given Special Solution of a Direct Method, and a Special Coefficient Linear Differential Equations L(y)=∑aiy(i)=∑bjejx into Ordinary Differential Equations Euler.

Evolution Solutions for the Ostrovsky Equation: A Perspective from an Auxiliary Elliptic Equation

2012 ◽  
Vol 538-541 ◽  
pp. 621-624
Author(s):  
Chun Huan Xiang
Keyword(s):  
Differential Equation ◽  
Elliptic Equation ◽  
Detailed Analysis ◽  
Periodic Solutions ◽  
Elliptic Function ◽  
Earth Rotation ◽  
Direct Method ◽  
Jacobi Elliptic Function ◽  
Ostrovsky Equation ◽  
A Direct Method

The Ostrovsky equation is used to describe the oceanic waves affected by Earth rotation. The auxiliary elliptic equation was employed as a direct method to construct the evolution solutions for the Ostrovsky equation in this manuscript. Detailed analysis of evolution solutions of the Ostrovsky equation is presented. The periodic solutions, which read Jacobi elliptic function solutions, hyperbolic solutions and trigonal solutions, are obtained. More parameters are included in the evolution solutions, the parameter space is enlarged. This method adds a new route to explore evolution solutions of nonlinear differential equation in a perspective from auxiliary elliptic equation.

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