Stability of negative solitary waves.
Stability of peakons for the generalized Camassa-Holm equation.
Stability of periodic waves in Hamiltonian PDEs
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg–de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for these waves is still in its infancy though. The issue has been tackled by various means. Of course, it is always possible to address stability from the spectral point of view. However, the link with nonlinear stability - in fact, orbital stability, since we are...
Stabilization of the Kawahara equation with localized damping
We study the stabilization of global solutions of the Kawahara (K) equation in a bounded interval, under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model. The proof requires of a unique continuation theorem and the smoothing effect of the (K) equation on the real line, which are proved in this work.
Stabilization of the Kawahara equation with localized damping
We study the stabilization of global solutions of the Kawahara (K) equation in a bounded interval, under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model. The proof requires of a unique continuation theorem and the smoothing effect of the (K) equation on the real line, which are proved in this work.
Stable time periodic solutions for damped sine-Gordon equations.
Supersymmetric representations and integrable fermionic extensions of the Burgers and Boussinesq equations.
Supersymmetry of affine Toda models as fermionic symmetry flows of the extended mkdv hierarchy.
Surfaces of Constant Curvature and Geometric Interpretations of the Klein-gordon, Sine-gordon and Sinh-gordon Equations
Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions.
The Cauchy problem for a short-wave equation.
The fifth-order Korteweg-de Vries equation.
The form factor program: a review and new results - the nested off-shell Bethe ansatz.
The Fourier spectral method for the Sivashinsky equation.
The generalized Burgers equation with and without a time delay.
The homogeneous balance of undetermined coefficients method and its application
The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can...
The local ill-posedness of the modified KdV equation
The nonlinear Klein-Gordon equation on an interval as a perturbed Sine-Gordon equation.
The Novikov-Veselov hierarchy of equations and integrable deformations of minimal Lagrangian tori in .
The Painlevé III equation and the Iwasawa decomposition.