Reality conditions of loop solitons genus : hyperelliptic am functions.
Reduced order controllers for Burgers' equation with a nonlinear observer
A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal...
Reductions of multicomponent mKdV equations on symmetric spaces of DIII-type.
Remark on well-posedness and ill-posedness for the KdV equation.
Remarks on global controllability for the Burgers equation with two control forces
Restricted flows and the soliton equation with self-consistent sources.
Results on qualitative features of periodic solutions of KdV
Riesz potentials for Korteweg-de Vries solitons and Sturm-Liouville problems.
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type.