Damped parametric oscillator and exactly solvable complex Burgers equations
نویسندگان
چکیده
منابع مشابه
Exactly solvable chaos in an electromechanical oscillator.
A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topolog...
متن کاملQuasi - Exactly - Solvable Differential Equations
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a representation as a polynomial element of the universal enveloping algebra of the algebra of differential (difference) operators in finitedimensional represent...
متن کاملQuasi Exactly Solvable Difference Equations
Several explicit examples of quasi exactly solvable ‘discrete’ quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known quasi exactly solvable systems, the harmonic oscillator (with/without the centrifugal potential) deformed by a sextic potential and the 1/ sin x potential de...
متن کاملComplex-Valued Burgers and KdV-Burgers Equations
Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T , there exists an explicit initial data such that its corresponding solution of the Burgers equation blows up at T . In addition, the global convergence and regularity of series solutions is established for initial data satisfying mil...
متن کاملQuasi-Exactly Solvable One-Dimensional Equations
Quasi-exactly solvable one-dimensional Schrödinger equations can be specified in order to exhibit supplementary analytic eigenstates. While the usual solutions are preserved by the sl(2,R) generators, the additional ones are stabilized at the level of the universal enveloping algebra of this Lie structure. We discuss the square-integrability, the orthogonality of these supplementary solutions a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2012
ISSN: 1742-6588,1742-6596
DOI: 10.1088/1742-6596/343/1/012020