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Geophysical Journal International, ISSN 0956-540X, 2016, Volume 204, Issue 2, pp. 1216 - 1221
This paper presents a generalized wave equation which unifies viscoelastic and pure elastic cases into a single wave equation. In the generalized wave... 
Seismic attenuation | Non-linear differential equation | Wave propagation | DISSIPATION | FREQUENCY-RANGE | LINEAR MODELS | GEOCHEMISTRY & GEOPHYSICS | MARINE-SEDIMENTS | ELASTIC WAVES | POWER-LAW ATTENUATION | LOSSY MEDIA | SOUND | PROPAGATION
Journal Article
Inverse Problems, ISSN 0266-5611, 12/2006, Volume 22, Issue 6, pp. 2197 - 2207
An inverse scattering method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless... 
BREAKING | MATHEMATICS, APPLIED | WAVES | INTEGRABILITY | CONSERVED QUANTITIES | SOLITON-SOLUTIONS | STABILITY | GEODESIC-FLOW | PHYSICS, MATHEMATICAL | SHALLOW-WATER EQUATION | PEAKONS | HIERARCHY | Physics - Exactly Solvable and Integrable Systems
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 09/2018, Volume 378-379, pp. 1 - 19
In this paper, we study entire solutions of the Allen–Cahn equation in one-dimensional Euclidean space. This equation is a scalar reaction–diffusion equation... 
Entire solution | Super–sub-solutions | Reaction–diffusion equation | Traveling front | REACTION-DIFFUSION EQUATIONS | MATHEMATICS, APPLIED | TRAVELING FRONTS | PHYSICS, MULTIDISCIPLINARY | Super-sub-solutions | PHYSICS, MATHEMATICAL | Reaction-diffusion equation | KPP EQUATION | NON-LINEAR DIFFUSION | SYSTEMS | Traveling | LATTICE
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2009, Volume 14, Issue 5, pp. 2034 - 2045
Journal Article
Physics Letters A, ISSN 0375-9601, 07/2016, Volume 380, Issue 33, pp. 2549 - 2560
In this paper flame instabilities are analyzed utilizing the Sivashinsky equation in order to derive the flame wrinkling factor. This is a synthetic variable... 
Sivashinsky equation | Flame modeling | Flame acceleration | Hydrogen | Flame instability | PHYSICS, MULTIDISCIPLINARY | SELF-ACCELERATION | DISCONTINUITIES | NON-LINEAR ANALYSIS | FRONTS | PREMIXED FLAMES | DYNAMICS | SURFACE | LAMINAR FLAMES | HYDRODYNAMIC INSTABILITY | Analysis | Wrinkling | Stability | Mathematical analysis | Solid state physics | Instability | Mathematical models | Acceleration
Journal Article
by Ito, K and Shu, HF
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 09/2018, Volume 51, Issue 38, p. 385401
The massive ordinary differential equation/integrable model (ODE/IM) correspondence is a relation between the linear problem associated with modified affine... 
PHYSICS, MULTIDISCIPLINARY | ODE/IM correspondence | DIFFERENTIAL-EQUATIONS | Q-OPERATORS | non-linear integral equation | FINITE-VOLUME SPECTRUM | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | Bethe ansatz equation | MODELS | W algebra | T-Q relation | STOKES MULTIPLIERS | affine Toda field equation | THERMODYNAMIC BETHE-ANSATZ
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2019, Volume 476, Issue 1, pp. 53 - 85
We consider the problem of global in time existence and uniqueness for the initial value problems for scaling parameters and a large class of initial data .... 
Stochastic multiplicative cascade | Branching processes | Non-uniqueness of solutions | Stochastic explosions | Stochastic recursion | Non-linear/non-local differential equations | MATHEMATICS | MATHEMATICS, APPLIED | UNIQUENESS
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 10/2016, Volume 206, Issue 1, pp. 57 - 108
A non-linear PDE featuring flux limitation effects together with those of the porous media equation (non-linear Fokker–Planck) is presented in this paper. We... 
Primary 35K57 | 35B36 | 34Cxx | 76B15 | 37Dxx | 35Q99 | Mathematics | 70Kxx | 35K67 | 37D50 | 35Q35 | Mathematics, general | Secondary 35B60 | FISHER-KPP EQUATIONS | MATHEMATICS | POPULATION-GENETICS | FRONTS | COMBUSTION | NON-LINEAR DIFFUSION | CONSERVATION-LAWS | MODEL | BURGERS-TYPE EQUATIONS | PROPAGATION | TRAVELING-WAVES
Journal Article
Geophysical Journal International, ISSN 0956-540X, 07/2018, Volume 214, Issue 1, pp. 58 - 69
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 12/2006, Volume 166, Issue 3, pp. 645 - 675
We prove, for the energy critical, focusing NLS, that for data whose energy is smaller than that of the standing wave, and whose homogeneous Sobolev norm H^1... 
Mathematics, general | Mathematics | EXISTENCE | MATHEMATICS | NON-LINEAR SCHRODINGER | MASS | CAUCHY-PROBLEM | CRITICAL POWER | TIME | COMPACTNESS | KLEIN-GORDON EQUATIONS | Mathematics - Analysis of PDEs
Journal Article
Journal of Guidance, Control, and Dynamics, ISSN 0731-5090, 07/2012, Volume 35, Issue 4, pp. 1025 - 1047
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 2019, Volume 52, Issue 3, p. 35202
We investigate dispersive and Strichartz estimates for the Schrodinger time evolution propagator e(-itH) on a star-shaped metric graph. The linear operator, H,... 
Schrodinger operator | quantum graphs | Strichartz estimates | non- linear Schrodinger equation | dispersion | LAPLACIANS | NETWORK | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | QUANTUM GRAPH | THIN FIBERS
Journal Article
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 03/2018, Volume 474, Issue 2211, pp. 20170687 - 20170687
Journal Article