Search results for "math-ph"
showing 10 items of 525 documents
N-order rational solutions to the Johnson equation depending on 2N - 2 parameter
2017
International audience; We construct rational solutions of order N depending on 2N-2 parameters. They can be written as a quotient of 2 polynomials of degree 2N(N+1) in x, t and 2N(N+1) in y depending on 2N-2 parameters. We explicitly construct the expressions of the rational solutions of order 4 depending on 6 real parameters and we study the patterns of their modulus in the plane (x,y) and their evolution according to time and parameters a1,a2,a3,b1,b2,b3.
Rational solutions to the Johnson equation of order N depending on 2N − 2 parameters
2019
We construct rational solutions of order N depending on 2N − 2 parameters. They can be written as a quotient of 2 polynomials of degree 2N (N + 1) in x, t and 4N (N + 1) in y depending on 2N − 2 parameters. We explicitly construct the expressions of the rational solutions of order 4 depending on 6 real parameters and we study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, b1, b2, b3.
Fredholm and wronskian representations of solutions to the Johnson equation and the third order case
2019
We construct solutions to the Johnson equation (J) by means of Fred-holm determinants first, then by means of wronskians of order 2N giving solutions of order N depending on 2N − 1 parameters. We obtain N order rational solutions which can be written as a quotient of two polynomials of degree 2N (N + 1) in x, t and 4N (N + 1) in y depending on 2N − 2 parameters. This method gives an infinite hierarchy of solutions to the Johnson equation. In particular, rational solutions are obtained. The solutions of order 3 with 4 parameters are constructed and studied in detail by means of their modulus in the (x, y) plane in function of time t and parameters a1, a2, b1, b2.
Multi-parametric families solutions to the Burgers equation
2021
We construct 2N real parameter solutions to the Burgers' equation in terms of determinant of order N and we call these solutions, N order solutions. We deduce general expressions of these solutions in terms of exponentials and study the patterns of these solutions in functions of the parameters for N = 1 until N = 4.
Geometric optimal control and two-level dissipative quantum systems
2009
International audience; The objective of this article is to present techniques of geometric time-optimal control developed to analyze the control of two-level dissipative quantum systems. Combined with numerical simulations they allow to compute the time-minimal control using a shooting method. The robustness with respect to initial conditions and dissipative parameters is also analyzed using a continuation method.
Time-Minimal Control of Dissipative Two-Level Quantum Systems: The Generic Case
2009
International audience; The objective of this article is to complete preliminary results from [5], [17] concerning the time-minimal control of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. The extremal system is described by a 3-D-Hamiltonian depending upon three parameters. We combine geometric techniques with numerical simulations to deduce the optimal solutions.
Geometric optimal control of dissipative quantum systems
2009
International audience
Geometric optimal control of spin systems
2010
International audience
Hamiltonian monodromy from a Gauss-Manin monodromy
2009
International audience
Optimal control of two-level dissipative quantum systems
2008
International audience