The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear parabolic partial differential equation for the optimal response function. We construct…
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48 results for “traveling wave solutions”
Study shows curves converge to traveling waves under specific conditions.
problem Global stability of traveling waves for area-preserving curvature flow.
method Area-preserving curvature flow with contact angle condition.
result Moving curves converge to traveling waves starting from embedded convex curves.
Classifies solitons for surface diffusion flow of graphs.
problem Classifying solitons for surface diffusion flow of graphs.
method Classifies solitons including equilibria, self-similar solutions, and travelling waves.
result Classified solitons for surface diffusion flow of entire graphs.
We give new results concerning the Frobenius integrability and solution of evolution equations admitting travelling wave solutions. In particular, we give a powerful result which explains the extraordinary integrability of some of these equations. We also discuss "local" conservations laws for evolution equations in ge…
Study on curves minimizing length in a degenerate metric plane.
problem Finding curves minimizing length in a plane with a degenerate metric.
method Established sufficient conditions for existence and non-existence of minimizers, using traveling wave solutions to a bi-stable Hamiltonian system.
result Existence and non-existence of minimizers can occur, with examples provided.
This paper solves a complex equation using Lie symmetry approach to find solitary wave and multiple soliton solutions.
problem Solving a (3 + 1)-dimensional KdV type equation.
method Lie group of transformation method to find infinitesimal generators and commutator table.
result Exact solutions of KdV type equation in explicit form.
We show that wave maps from two-dimensional Minkowski space to hyperbolic spaces $\H^m$ are globally smooth in time if the initial data is smooth, conditionally on some reasonable claims concerning the local theory of such wave maps, as well as the self-similar and travelling (or stationary solutions); w…
Study traveling waves in hyperbolic space for Fisher-KPP equations.
problem Understanding wave behavior in hyperbolic space for Fisher-KPP equations.
method Analyzes the Cauchy problem in hyperbolic space for heat equation with Fisher-KPP forcing term.
result Proves new results on the dichotomy of solution propagation or vanishing based on diffusion and reaction strength.
Researchers recover material parameters in transversely isotropic media from travel times of qP and qSV waves.
problem Recovering material parameters in transversely isotropic media from travel times of qP and qSV waves.
method Using parabolic type operators and stability estimates for travel times of qP and qSV waves.
result Stability estimates for recovering material parameters from travel times of qP and qSV waves.
Travelling wave solutions of an equation of Harry Dym type arising in the Black-Scholes frameworkmath.NA
The study finds solutions to a financial equation related to volatility.
problem Finding solutions to a financial equation related to volatility.
method Using a zero-curvature condition and soliton theory, the study derives a variant of the Harry Dym equation and finds its travelling wave solutions.
result A family of travelling wave solutions to a variant of the Harry Dym equation is found.
Model for corporate bond pricing with credit rating migration, solving a double free boundary problem.
problem Corporate bond pricing with credit rating migration risks.
method Established a pricing model as a double free boundary problem, proving existence, uniqueness, and regularity of the solution.
result Two free boundaries are shown to be smooth and converge to a traveling wave solution as time goes to infinity.
In this paper we construct a parametrix for the forward fundamental solution of the wave and Klein-Gordon equations on asymptotically de Sitter spaces without caustics. We use this parametrix to obtain asymptotic expansions for solutions of the inhomogeneous equation and to obtain a uniform L^p estimate for a family of…
Determining Finsler manifold structure from boundary distance map and elastic wave measurements.
problem Determine the structure of a compact Finsler manifold from its boundary distance map.
method Construct optimal fiberwise open subset of tangent bundle, use inverse problem in elasticity to measure travel times of waves.
result Finsler function can be uniquely determined from boundary distance map and travel times of waves.
Develops methods to construct harmonic and wave maps into variable-curvature surfaces.
problem Limited explicit constructions for harmonic and wave maps in variable-curvature settings.
method Reduction framework for pseudo-Riemannian surfaces, geometric ansatz, first-order ODEs.
result Constructs explicit harmonic and wave maps into ellipsoids, hyperboloids, and Schwarzschild exterior.
Paper recovers material parameters in transversely isotropic media under specific conditions.
problem Recovering material parameters in transversely isotropic media.
method Knowledge of qSH wave travel times determines the axis of isotropy and some elastic material parameters.
result Full determination of material parameters under certain conditions.
The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup-Kupershmidt hierarchy is constructed. The integration of the congruence curves is discussed. Local motions defined by the traveling wave…
Study classifies traveling solitary waves in energy-critical half-wave maps.
problem Energy-critical half-wave maps into .
method Geometric characterization, conformal Möbius group, Jacobi operators.
result Explicit classification and detailed analysis of traveling solitary waves.
Researchers recover Riemannian manifolds and lower order terms from travel time data.
problem Recovering Riemannian manifolds and lower order terms from travel time data.
method Adaptation of the Boundary Control method to recover lower order terms.
result Complete Riemannian manifolds and lower order terms can be uniquely recovered from a local source to solution map.
Study on determining medium properties from wave travel times.
problem Determine anisotropic index of refraction from travel times.
method Geometry problems, boundary rigidity, lens rigidity, tensor tomography.
result Recent results on partial data in boundary and lens rigidity.
New method clusters travel behavior data from 1990-2017.
problem Challenges in analyzing large-scale travel data.
method Divide and Combine K-means clustering on time series data.
result Activity-travel patterns can be grouped into three clusters.
Recovering the isometry type of a Riemannian manifold from local boundary diffraction travel timesmath.AP
We analyze the inverse problem, originally formulated by Dix in geophysics, of reconstructing the wave speed inside a domain from boundary measurements associated with the single scattering of seismic waves. We consider a domain with a varying and possibly anisotropic wave speed which we model as a Riemannia…
We study an equation lying `mid-way' between the periodic Hunter-Saxton and Camassa-Holm equations, and which describes evolution of rotators in liquid crystals with external magnetic field and self-interaction. We prove that it is an Euler equation on the diffeomorphism group of the circle corresponding to a natural r…
Rotational elasticitymath-ph
We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which give…
In this paper we propose and analyze a method based on the Riccati transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation arising from the stochastic dynamic optimal allocation problem. We show how the fully nonlinear Hamilton-Jacobi-Bellman equation can be transformed into a quasi-linear paraboli…
LPINNs solve complex PDEs by reformulating PINNs on Lagrangian frame, reducing training complexity.
problem Complexity in training PINNs, especially for convection-diffusion equations.
method Propose LPINNs, a Lagrangian reformulation of PINNs, with two branches solving state variables and characteristics curves.
result Loss landscapes of LPINNs are less sensitive to problem complexity compared to traditional PINNs.
Researchers reconstruct simple Riemannian manifolds from boundary wave arrival times.
problem Reconstructing Riemannian manifolds from unknown interior sources and arrival times.
method Discrete metric approximation using labeled Gromov--Hausdorff distance.
result Finite-time approximations converge to the true Riemannian manifold.
Explicitly describes pseudospherical helicoids and their topological embeddings.
problem Solving a problem posed by Popov regarding pseudospherical surfaces.
method Explicitly describes pseudospherical helicoids in terms of elliptic functions.
result Countably many continuous families of topologically embedded pseudospherical helicoids constructed.
Boosting algorithms improve delivery time prediction in postal services.
problem Challenges in long-term travel time prediction for postal services.
method Investigated linear regression models, tree-based ensembles (random forest, bagging, boosting), and compared their performance.
result Boosting algorithms, especially light gradient boosting and catboost, outperform other methods in accuracy and runtime efficiency.
Researchers prove injectivity and stability for mixed ray transform on simple manifolds.
problem Injectivity and stability of mixed ray transform for tensor fields.
method Analyzing tensor fields on 3D compact simple Riemannian manifolds with boundary.
result Injectivity and stability estimates for normal operator on generic 3D simple manifolds.
Unique solutions found for wave-like decaying null infinity equations.
problem Wave-like decaying null infinity equations with spherically symmetric Einstein-scalar-field.
method Local and global unique solutions for small initial data.
result Sharp decaying condition for unique solutions.
Classifies solutions to vacuum weighted Einstein equations on pr-waves.
problem Classifying solutions to vacuum weighted Einstein field equations on pr-waves.
method Classifying solutions using smooth metric measure spacetimes of dimension 4.
result Provides examples of solutions with special geometric properties.
Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.
problem Interaction of three impulsive gravitational waves in Einstein vacuum equations.
method Geometric estimates and wave estimates to prove local solution and continuity.
result Local solution to Einstein vacuum equations with three impulsive gravitational waves, Lipschitz continuity.
Global solution found for biharmonic wave maps into spheres.
problem Solving biharmonic wave maps into spherical targets.
method Reformulated as a conservation law, solved with Ginzburg-Landau approximation.
result Global weak solution constructed in the energy space.
The paper tackles hierarchical reinforcement learning by approximating optimal solutions for the Traveling Salesman Problem.
problem Approximating optimal solutions for the Traveling Salesman Problem using hierarchical reinforcement learning.
method Mapping the problem into a Reward Discounted Traveling Salesman Problem and deriving approximate solutions using local policies.
result Three stochastic policies are proposed that guarantee better performance than any deterministic policy.
The paper solves a dynamic portfolio optimization problem using Riccati transformation.
problem Dynamic stochastic portfolio optimization involving expected and intertemporal utilities.
method Solving a fully nonlinear HJB equation through Riccati transformation into a quasi-linear parabolic equation.
result The numerical method based on semi-implicit scheme converges at second order.
Paper explores non-uniqueness and uniqueness class for wave equations on graphs.
problem Non-uniqueness of solutions to wave equations on infinite graphs.
method Analyticity of solutions in the uniqueness class, extension to a wide class of linear evolution equations.
result Sharp uniqueness class for solutions of wave equations on graphs.
Deep RL learns 2-opt heuristics to improve TSP solutions.
problem Improving TSP solutions beyond initial heuristics.
method Deep reinforcement learning to learn 2-opt operations.
result Learned policies improve solutions faster than previous methods.
Neural network solves M-TSP with varying sets.
problem Generalizing TSP to M-TSP.
method Pooling networks combining set and graph elements, with new loss and layers.
result Outperforms leading solver's meta-heuristics.
Measuring wave sources uniquely identifies manifold properties.
problem Determining Riemannian manifold structure from wave observations.
method Semilinear wave equation measurements at a single point.
result Topological, differential, and geometric structure can be inferred.
Geometric flow on curves in S^3 generates YO equations solutions.
problem Modeling short wave-long wave interaction.
method Simple geometric flow on curves in .
result Constructs transverse curves for YO equations periodic solutions.
Constructs periodic solutions for wave equations, including Einstein's, with negative cosmological constant.
problem Finding periodic solutions for nonlinear wave equations, especially Einstein's equations with negative cosmological constant.
method Analytic continuation to construct periodic solutions.
result Infinite-dimensional families of time-periodic solutions for vacuum and Einstein-Maxwell-dilaton-scalar fields.
Graph Neural Networks and Guided Local Search improve TSP solutions.
problem Finding optimal solutions to the Traveling Salesperson Problem quickly.
method Hybrid approach combining Graph Neural Networks and Guided Local Search.
result Significant reduction in optimality gap for TSP solutions.
Study on blow-up solutions for semilinear wave equations on specific manifolds.
problem Investigate blow-up and lifespan estimates for semilinear wave equations on asymptotically Euclidean manifolds.
method Use of exponential perturbation metric and construction of entire solutions for a related equation.
result Sharp upper bound estimates for the lifespan of solutions.
Recently, a novel adaptive wave model for financial option pricing has been proposed in the form of adaptive nonlinear Schrödinger (NLS) equation [Ivancevic a], as a high-complexity alternative to the linear Black-Scholes-Merton model [Black-Scholes-Merton]. Its quantum-mechanical basis has been elaborated in [Ivancevi…
In this paper we deal with quadratic metric-affine gravity, which we briefly introduce, explain and give historical and physical reasons for using this particular theory of gravity. Further, we introduce a generalisation of well known spacetimes, namely pp-waves. A classical pp-wave is a 4-dimensional Lorentzian spacet…
Study reconstructs Riemannian metric from Cherenkov radiation in complex media.
problem Reconstructing internal geometry of inhomogeneous anisotropic targets.
method Mathematical model of waves in medium, including vector-valued wave operator and phase velocity.
result Riemannian metric inside a bounded region can be reconstructed from boundary measurements of Cherenkov radiation.
Proves wave equation solutions in Kerr-de Sitter spacetime have specific asymptotic expansions.
problem Analyzing solutions to wave equations in Kerr-de Sitter spacetime.
method Developed a Fredholm setup for quasinormal modes and analyzed trapping of lightlike geodesics.
result Proves asymptotic expansions of wave equation solutions up to a decay order.
A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing 'controlled Brownian behavior' of financial markets, is formally defined by adaptive nonlinear Schrödinger (NLS) equations, defining the option-pricing wave function in terms of the stock…