Nonlinear Evolution Equations for Second-order Spectral Problem

2012 ◽  
Vol 7 (9) ◽  
Author(s):  
Wei Liu ◽  
Shujuan Yuan ◽  
Shuhong Wang
Keyword(s):  
Spectral Problem ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Second Order ◽  
Nonlinear Evolution Equations

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.

scholarly journals Matrix spectral problem with multiple-order jumps and poles

1996 ◽  
Vol 37 (3) ◽  
pp. 320-333 ◽  
Author(s):  
Zhuhan Jiang
Keyword(s):  
Spectral Problem ◽  
Spectral Data ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Temporal Dimension ◽  
Explicit Representations ◽  
Inverse Spectral Method ◽  
Matrix Spectral Problem

AbstractThe inverse spectral method for a general N × N spectral problem for solving nonlinear evolution equations in one spacial and one temporal dimension is extended to include multi-boundary jumps and high-order poles and their explicit representations. It therefore provides a formalism to generate soliton solutions that correspond to higher-order poles of the spectral data.

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