Exact boundary controllability for higher order nonlinear Schrödinger equations with constant coefficients.
Exact boundary controllability of 3-D Euler equation
Exact boundary controllability of 3-D Euler equation
We prove the exact boundary controllability of the 3-D Euler equation of incompressible inviscid fluids on a regular connected bounded open set when the control operates on an open part of the boundary that meets any of the connected components of the boundary.
Exact boundary controllability of a nonlinear KdV equation with critical lengths
We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations
Exact controllability in projections for three-dimensional Navier–Stokes equations
Exact propagators for soliton potentials.
Exact solutions and localized structures for higher-dimensional Burgers systems.
Exact solutions and symmetry operators for the nonlocal Gross-Pitaevskii equation with quadratic potential.
Exact solutions for a new fifth-order integrable system.
Exact solutions for a third-order KdV equation with variable coefficients and forcing term.
Exact solutions for equations of Bose-Fermi mixtures in one-dimensional optical lattice.
Exact solutions for the generalized BBM equation with variable coefficients.
Exact solutions of steady plane flows using -coordinates.
Exact solutions of steady plane MHD aligned flows using - or -coordinates.
Exact solutions of the generalized Benjamin-Bona-Mahony equation.
Exact solutions to KdV6 equation by using a new approach of the projective Riccati equation method.
Examples of discontinuous, divergence-free solutions to elliptic variational problems
We give an example of a bounded discontinuous divergence-free solution of a linear elliptic system with measurable bounded coefficients in and a corresponding example for a Stokes-like system.
Excess charge for pseudo-relativistic atoms in Hartree-Fock theory.
Existence and analyticity of lump solutions for generalized Benney-Luke equations.