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Structure-preserving algorithms for solving conservative PDEs with addedlinear dissipation are generalized to systems with time-dependentdamping/driving terms. This study is motivated by several PDE models ofphysical phenomena, such as Korteweg-de Vries, Klein-Gordon, Schr\"{o}dinger,and Camassa-Holm equations, all with damping/driving terms and time-dependentcoefficients. Since key features of the PDEs under consideration are describedby local conservation laws, which are independent of the boundary conditions,the proposed (second-order in time) discretizations are developed with theintent of preserving those local conservation laws. The methods arerespectively applied to a damped-driven nonlinear Schr\"{o}dinger equation anda damped Camassa-Holm equation. Numerical experiments illustrate thestructure-preserving properties of the methods, as well as favorable resultsover other competitive schemes.

Exponential Integrators Preserving Local Conservation Laws of PDEs with Time-Dependent Damping/Driving Forces