Search results for "Nonlinear wave equation"

showing 4 items of 4 documents

The Bethe ansatz and the Tzitzéica–Bullough–Dodd equation

2012

The theory of classically integrable nonlinear wave equations, and the Bethe Ansatz systems describing massive quantum field theories defined on an infinite cylinder, are related by an important mathematical correspondence that still lacks a satisfactory physical interpretation. In this paper we shall describe this link for the case of the classical and quantum versions of the (Tzitz\'eica-)Bullough-Dodd model.

High Energy Physics - TheoryPhysicsQuantum PhysicsQuantum sigma modelsIntegrable system010308 nuclear & particles physicsGeneral MathematicsGeneral EngineeringGeneral Physics and AstronomyODE/IM correspondenceQuantum sigma models ODE/IM correspondence01 natural sciencesBethe ansatzNonlinear Sciences::Exactly Solvable and Integrable SystemsNonlinear wave equation0103 physical sciencesCylinderQuantum field theory010306 general physicsMathematical PhysicsMathematical physicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance

2014

5 pags.; 5 figs.; PACS number(s): 46.40.−f, 47.20.Ky, 47.35.−i, 47.52.+j

PhysicsNonlinear systemModulational instabilityClassical mechanicsNonlinear wave equationWave resonancePeregrine solitonAstrophysics::Cosmology and Extragalactic AstrophysicsRogue waveParametric statisticsPhysical Review E
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A blow-up result for a nonlinear wave equation on manifolds: the critical case

2021

We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.

manifoldApplied MathematicsBlow-upMathematical analysisBoundary (topology)Riemannian manifoldWave equationManifoldcritical caseDimension (vector space)Settore MAT/05 - Analisi MatematicaNonlinear wave equationMathematics::Differential Geometryinhomogeneous semilinear wave equationAnalysisMathematicsApplicable Analysis
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Modelling of rotations by using matrix solutions of nonlinear wave equations

2007

A family of matrix solutions of nonlinear wave equations is extended and its application to modelling is given. It is shown that a similarity transformation, induced by the matrix solution, is equivalent to the rotation. Matrix solutions are used for modelling helical motions and vortex rings, simultaneous rotations and particles collision, mapping contraction and pulsating spheres. Geometrical interpretation of the doubling of rotation angle in each step of sequential mapping contraction is given. First Published Online: 14 Oct 2010

mapping contractionanti‐commuting matricesMathematical analysisMatrix solutionparticles collisionCollisionrotationMatrix similarityVortex ringClassical mechanicsnonlinear wave equationNonlinear wave equationvortex ringModeling and SimulationQA1-939SPHERESmatrix solutionContraction (operator theory)AnalysisMathematicsMathematicsMathematical Modelling and Analysis
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