scholarly journals Optimality conditions for systems driven by nonlinear evolution equations

1995 ◽  
Vol 1 (1) ◽  
pp. 27-36
Author(s):  
N. Papageorgiou
Keyword(s):  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Optimal Control Problems ◽  
Nonlinear Evolution ◽  
Sufficient Conditions ◽  
Nonlinear Evolution Equations ◽  
Control Problems ◽  
Terminal Constraints ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient

Using the Dubovitskii-Milyutin theory we derive necessary and sufficient conditions for optimality for a class of Lagrange optimal control problems monitored by a nonlinear evolution equation and involving initial and/or terminal constraints. An example of a parabolic control system is also included.

scholarly journals Combined Exp-Function Ansatz Method and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
Gui Mu ◽  
Jun Liu ◽  
Zhengde Dai ◽  
Xi Liu
Keyword(s):  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Bilinear Forms ◽  
Hyperbolic Functions ◽  
Ansatz Method ◽  
New Type ◽  
Hirota Bilinear ◽  
Multisoliton Solutions

Our aim is to present a combined Exp-function ansatz method. This method replaces the traditional assumptions of multisolitons by a combination of the hyperbolic functions and triangle functions in Hirota bilinear forms of nonlinear evolution equation. Using this method, we can obtain many new type analytical solutions of various nonlinear evolution equations including multisoliton solutions as well as breath-like solitons solutions. These solutions will exhibit interesting dynamic diversity.

Application of Improved (G′/G)–Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations

2012 ◽  
Vol 4 (1) ◽  
pp. 122-130 ◽  
Author(s):  
Xiaohua Liu ◽  
Weiguo Zhang ◽  
Zhengming Li
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
The Other ◽  
Wave Solutions

AbstractIn this work, the improved (G′/G)-expansion method is proposed for constructing more general exact solutions of nonlinear evolution equation with the aid of symbolic computation. In order to illustrate the validity of the method we choose the RLW equation and SRLW equation. As a result, many new and more general exact solutions have been obtained for the equations. We will compare our solutions with those gained by the other authors.

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