Nonautonomous <i>k</i>-contact field theories
Xavier Rivas
Abstract
This paper provides a new geometric framework to describe non-conservative field theories with explicit dependence on the space–time coordinates by combining the k-cosymplectic and k-contact formulations. This geometric framework, the k-cocontact geometry, permits the development of Hamiltonian and Lagrangian formalisms for these field theories. We also compare this new formulation in the autonomous case with the previous k-contact formalism. To illustrate the theory, we study the nonlinear damped wave equation with external time-dependent forcing.
Topics & Concepts
Rotation formalisms in three dimensionsHamiltonian formalismFormalism (music)LagrangianHamiltonian (control theory)Nonlinear systemClassical mechanicsMathematicsCovariant Hamiltonian field theoryField (mathematics)Classical field theoryField equationHamiltonian systemTheoretical physicsPhysicsMathematical analysisMathematical physicsGeometryPure mathematicsQuantum mechanicsCovariant transformationGravitational fieldMathematical optimizationMusicalArtVisual artsNumerical methods for differential equationsNonlinear Photonic SystemsNonlinear Waves and Solitons