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.
The Painlevé test and reducibility to the canonical forms for higher-dimensional soliton equations with variable-coefficients.
The PDE describing constant mean curvature surfaces
We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.
The solution of general KdV equation in a class of steplike functions.
The SQP method for control constrained optimal control of the Burgers equation
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...
The SQP method for control constrained optimal control of the Burgers equation
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...
Three-dimensional Korteweg-de Vries equation and traveling wave solutions.
Traduzione in equazioni integrali di un problema analogo al problema biarmonico fondamentale
Transparent potentials and hamiltonian systems
Transverse nonlinear instability for two-dimensional dispersive models
Traveling wave solutions of Burgers equation for power-law non-Newtonian flows.