First and second order nonlinear evolution equations from an inverse spectral problem

1993 ◽  
Vol 9 (1) ◽  
pp. 1-37 ◽  
Author(s):  
M Boiti ◽  
F Pempinelli ◽  
P C Sabatier
Keyword(s):  
Spectral Problem ◽  
Evolution Equations ◽  
Inverse Spectral Problem ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Evolution Equations ◽  
Inverse Spectral

An extension of the coupled derivative nonlinear Schrödinger hierarchy

2018 ◽  
Vol 32 (02) ◽  
pp. 1850016
Author(s):  
Siqi Xu ◽  
Xianguo Geng ◽  
Bo Xue
Keyword(s):  
Conservation Laws ◽  
Spectral Problem ◽  
Compatibility Condition ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Trace Identity ◽  
Hamiltonian Structures ◽  
Nonlinear Schrödinger ◽  
Matrix Spectral Problem

In this paper, a 3 × 3 matrix spectral problem with six potentials is considered. With the help of the compatibility condition, a hierarchy of new nonlinear evolution equations which can be reduced to the coupled derivative nonlinear Schrödinger (CDNLS) equations is obtained. By use of the trace identity, it is proved that all the members in this new hierarchy have generalized bi-Hamiltonian structures. Moreover, infinitely many conservation laws of this hierarchy are constructed.

scholarly journals Optimal control of nonlinear second order evolution equations

1993 ◽  
Vol 6 (2) ◽  
pp. 123-135 ◽  
Author(s):  
N. U. Ahmed ◽  
Sebti Kerbal
Keyword(s):  
Optimal Control ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Evolution Equations ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Lagrange Problem

In this paper we study the optimal control of systems governed by second order nonlinear evolution equations. We establish the existence of optimal solutions for Lagrange problem.

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