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Nonlinear Contraction Tools for Constrained Optimization
Nonlinear dynamics nonlinear control constrained optimization Lagrange parameters sliding control
2012/6/30
This paper describes new results linking constrained optimization theory and nonlinear contraction analysis. Generalizations of Lagrange parameters are derived based on projecting system dynamics on t...
A Family of Exact, Analytic Time Dependent Wave Packet Solutions to a Nonlinear Schroedinger Equation
A Family of Exact Analytic Time Dependent Packet Solutions Nonlinear Schroedinger Equation Mathematical Physics
2012/6/19
We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schr\"odinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The N...
Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation
Relativistic point dynamics Einstein formula nonlinear Klein-Gordon equation Mathematical Physics
2012/6/15
Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems wh...
Actions for an Hierarchy of Attractive Nonlinear Oscillators Including the Quartic Oscillator in 1+1 Dimensions
Actions Hierarchy of Attractive Nonlinear Oscillators the Quartic Oscillator 1+1 Dimensions Mathematical Physics
2012/4/23
In this paper, we present an explicit form in terms of end-point data for the classical action $S_{2n}$ evaluated on extremals satisfying the Hamilton-Jacobi equation for each member of a hierarchy of...
On the Rigorous Derivation of the 3D Cubic Nonlinear Schr鰀inger Equation with A Switchable Quadratic Trap
Gross-Pitaevskii Hierarchy Switchable Quadratic Trap Collapsing Estimate Klainerman-Machedon Board Game and Space-time Bound
2012/4/17
We consider the dynamics of the 3D N-body Schr\"odinger equation in the presence of a switchable quadratic trap. We assume the pair interaction potential is N^{3{\beta}-1}V(N^{{\beta}}x). We justify t...
Nonlinear self-adjointness and conservation laws
Conservation laws Nonlinear self-adjointness Diffusion Kompaneets equation KP equation
2011/9/20
Abstract: The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self...
Traveling kinks in dissipative nonlinear dynamics
dissipative nonlinear dynamics Mathematical Physics
2011/9/20
Abstract: Ginzburg-Landau free energy functionals frequently encountered in several fields of physics lead to nonlinear cubic Euler-Lagrange equation of motion of damped type in the traveling variable...
Stationary Nonlinear Schrodinger Equation on Simplest Graphs: Boundary conditions and exact solutions
Nonlinear Schrodinger Equation Simplest Graphs Mathematical Physics
2011/9/29
Abstract: We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs co...
Complete group classification of a class of nonlinear wave equations
Complete group classification nonlinear wave equations Analysis of PDEs
2011/7/26
Abstract: Preliminary group classification became prominent as an approach to symmetry analysis of differential equations due to the paper by Ibragimov, Torrisi and Valenti [J. Math. Phys. 32, 2988-29...
Nonlinear Boundaries in Quantum Mechanics
Nonlinear Boundaries Quantum Mechanics Quantum Physics
2011/7/28
Abstract: Based on empirical evidence, quantum eigenvalue equations appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a ...
Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction
Hierarchy of integrable Hamiltonians nonlinear n-wave interaction Exactly Solvable and Integrable Systems
2011/7/26
Abstract: In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special...
Asymptotic Analysis and Synthesis in Mechanics of Solids and Nonlinear Dynamics
Asymptotic Analysis Synthesis Mechanics of Solids Nonlinear Dynamics
2011/7/26
Asymptotic Analysis and Synthesis in Mechanics of Solids and Nonlinear Dynamics.
Breathers and solitons of generalized nonlinear Schrodinger equations as degenerations of algebro-geometric solutions
Breathers solitons nonlinear Schrodinger equations Analysis of PDEs
2011/7/25
Abstract: We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton...
A solution of the Gross-Witten matrix model by nonlinear random processes
imulation methods planar approximation lattice field theory random processes
2011/1/14
We illustrate the stochastic method for solving the Schwinger-Dyson equations in large-N quantum field theories described in ArXiv:1009.4033 on the example of the Gross-Witten unitary matrix model.
On integrability of variable coefficient nonlinear Schrodinger equations
variable coefficient nonlinear Schrodinger Lax pairs technique group-theoretical
2010/4/21
We apply Painlev\'e test to the most general variable coefficient nonlinear Schrodinger (VCNLS) equations as an attempt to identify integrable classes and compare our results versus those obtained by ...