We study stability of N-soliton solutions of the FPU lattice equation. Solitary wave solutions of FPU cannot be characterized as a critical point of conservation laws due to the lack of infinitesimal invariance in the spatial variable. In place of standard variational arguments for Hamiltonian systems, we use an exponential stability property of the linearized FPU equation in a weighted space w...

We generalize the Toda lattice (or Toda chain) equation to the square lattice, i.e., we construct an integrable nonlinear equation for a scalar field taking values on the square lattice and depending on a continuous (time) variable, characterized by an exponential law of interaction in both discrete directions of the square lattice. We construct the Darboux-Bäcklund transformations for such lat...

abstract rockfill dams are a type of hydraulic control structures used to protect river bed in cases where a considerable reservoir volume is available behind these structures; it could mitigate the floods and provide a gradual depletion of incoming volume of water so that the discharge passing downstream is decreased. one of the main issues on utilizing rockfill dams is to keep its permeabilit...

We propose a dimensionality reduction method for infinite–dimensional measure– valued evolution equations such as the Fokker-Planck partial differential equation or the Kushner-Stratonovich resp. Duncan-Mortensen-Zakai stochastic partial differential equations of nonlinear filtering, with potential applications to signal processing, quantitative finance, heat flows and quantum theory among many...

Keywords: Differential equations Difference equations Stability Bohl–Perron theorem Linear delay dynamic equations Time scales Uniform exponential stability a b s t r a c t This paper is concerned with the uniform exponential stability of ordinary and delay dynamic equations. After revealing the equivalence between various types of uniform exponential stability definitions on time scales with b...

We are concerned with the exponential mean-square stability of two-step Maruyama methods for stochastic differential equations with time delay. We propose a family of schemes and prove that it can maintain the exponential mean-square stability of the linear stochastic delay differential equation for every step size of integral fraction of the delay in the equation. Numerical results for linear ...

We prove that the standard conditions that provide unique solvability of a mixed stochastic differential equations also guarantee that its solution possesses finite moments. We also present conditions supplying existence of exponential moments. For a special equation whose coefficients do not satisfy the linear growth condition, we find conditions for integrability of its solution. Keywors. Mix...

Kinetic analyses for LD have been performed by use of a centrifugal analyzer. These analyses were performed on clinical control sera and human sera at 340 nm and 30#{176}C. Evaluation of the data with both linear and nonlinear equations demonstrates that the exponential equation (y = C Ac5) gives a lower value for “root mean square” (better fit) for the activity at high levels than does the lin...

This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equ...

While the exponential learning equation, indicating a gradually diminishing improvement, is one of the standard equations to describe learning, a sigmoid behavior with initially increasing then decreasing improvement has also been suggested. Herewe show that the sigmoid behavior ismathematically derived from the standard exponential equation when the independent variable of the equation is rest...