Numerical Study of Nonlinear Equations with Infinite Number of Derivatives

Abstract

We study equations with infinitely many derivatives. Equations of this type form a new class of equations in mathematical physics. These equations originally appeared in p-adic and later in fermionic string theories and their investigation is of much interest in mathematical physics and applications, in particular in cosmology. Differential equation with infinite number of derivatives could be written as nonlinear integral equations. We perform numerical investigation of solutions of the equations. It is established that these equations have two different regimes of the solutions: interpolating and periodic. The critical value of the parameter q separating these regimes is found to be q^2=1.37. Convergence of iterative procedure for these equations is proved.

23 pages, 10 figures

References in corpus (2)

• Time Evolution in Superstring Field Theory on non-BPS brane.I. Rolling Tachyon and Energy-Momentum Conservation
• Stress Tensors in p-adic String Theory and Truncated OSFT

Cited by in corpus (43)

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• p-adic Inflation
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• Bouncing and Accelerating Solutions in Nonlocal Stringy Models
• Nonlocal gravity and the diffusion equation
• Towards LHC Physics with Non-local Standard Model
• Large Nongaussianity from Nonlocal Inflation
• Dynamics in Nonlocal Cosmological Models Derived from String Field Theory
• Time Lumps in Nonlocal Stringy Models and Cosmological Applications
• Thermal Duality and Hagedorn Transition from p-adic Strings
• Cosmological tachyon from cubic string field theory
• Non-local SFT Tachyon and Cosmology
• Tachyon condensation in open-closed p-adic string theory
• Cosmic acceleration and crossing of w=-1 barrier in non-local Cubic Superstring Field Theory model
• Nonlinear equations for p-adic open, closed, and open-closed strings
• Diffusing non-local inflation: Solving the field equations as an initial value problem
• Taming the Tachyon in Cubic String Field Theory
• Thermodynamics and Cosmological Constant of Non-Local Field Theories from p-Adic Strings
• Stringy Dark Energy Model with Cold Dark Matter
• Nonlocal instantons and solitons in string models
• Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric
• Cosmological Daemon
• Toward Open-Closed String Theoretical Description of Rolling Tachyon
• Rolling Tachyon Solution in Vacuum String Field Theory
• Dynamics with Infinitely Many Time Derivatives in Friedmann-Robertson-Walker Background and Rolling Tachyon
• Kinks of open superstring field theory
• Localization of nonlocal cosmological models with quadratic potentials in the case of double roots
• Cosmological rolling solutions of nonlocal theories
• Bouncing universe with the non-minimally coupled scaler field and its reconstructing
• Thermodynamics of String Field Theory Motivated Nonlocal Models
• Towards p-Adic String in Constant B-Field
• Pure Gauge Configurations and Tachyon Solutions to String Field Theories Equations of Motion
• Exact noncommutative solitons in p-adic strings and BSFT
• Energy Flow from Open to Closed Strings in a Toy Model of Rolling Tachyon
• Non-local scalar fields in static spacetimes via heat kernels
• Quintessence Dark Energy from strongly-coupled Higgs mass gap: Local and Non-local higher-derivative non-perturbative scenarios
• FRW Cosmology with Non-positively Defined Higgs Potentials
• Topological defects in nonlocal field theories