• Derivation of Boussinesq's shoaling law using a coupled BBM system 

      Kalisch, Henrik; Senthilkumar, Amutha (Peer reviewed; Journal article, 2013-03-14)
      This paper is focused on finding rules for waveheight change in a solitary wave as it runs up a slowly increasing bottom. A coupled BBM system is used to describe the solitary waves. Expressions for energy density and ...
    • Existence and uniqueness of singular solutions for a conservation law arising in magnetohydrodynamics 

      Kalisch, Henrik; Mitrovic, Darko; Teyekpiti, Vincent (Peer reviewed; Journal article, 2018-10-30)
    • Laboratory Experiments on Internal Solitary Waves in Ice-Covered Waters 

      Carr, Magda; Sutherland, P.; Haase, A.; Evers, K.-U.; Fer, Ilker; Jensen, Atle; Kalisch, Henrik; Berntsen, Jarle; Parau, E.; Thiem, Ø.; Davies, P.A. (Peer reviewed; Journal article, 2019)
      Internal solitary waves (ISWs) propagating in a stably stratified two‐layer fluid in which the upper boundary condition changes from open water to ice are studied for grease, level, and nilas ice. The ISW‐induced current ...
    • Non-standard shocks in the Buckley-Leverett equation 

      Kalisch, Henrik; Mitrovic, Darko; Nordbotten, Jan Martin (Peer reviewed; Journal article, 2015-08)
      It is shown how delta shock waves which consist of Dirac delta distributions and classical shocks can be used to construct non-monotone solutions of the Buckley–Leverett equation. These solutions are interpreted using a ...
    • Numerical bifurcation for the capillary Whitham equation 

      Remonato, Filippo; Kalisch, Henrik (Journal article, 2017-03)
      The so-called Whitham equation arises in the modeling of free surface water waves, and combines a generic nonlinear quadratic term with the exact linear dispersion relation for gravity waves on the free surface of a fluid ...
    • A numerical study of nonlinear dispersive wave models with SpecTraVVave 

      Kalisch, Henrik; Moldabayev, Daulet; Verdier, Olivier (Peer reviewed; Journal article, 2017-03-02)
      In nonlinear dispersive evolution equations, the competing effects of nonlinearity and dispersion make a number of interesting phenomena possible. In the current work, the focus is on the numerical approximation of ...
    • On the Formulation of Mass, Momentum and Energy Conservation in the KdV Equation 

      Ali, Alfatih Mohammed A.; Kalisch, Henrik (Peer reviewed; Journal article, 2014-10)
      The Korteweg-de Vries (KdV) equation is widely recognized as a simple model for unidirectional weakly nonlinear dispersive waves on the surface of a shallow body of fluid. While solutions of the KdV equation describe the ...
    • On the shoaling of solitary waves in the KdV equation 

      Khorsand, Zahra; Kalisch, Henrik (Conference object; Peer reviewed, 2014)
      The waveheight change in surface waves with a sufficiently slow variation in depth is examined. Using a new formulation of the energy flux associated to waves modeled by the Korteweg-de Vries equation, a system of three ...
    • PDE Based Algorithms for Smooth Watersheds 

      Hodneland, Erlend; Tai, Xue-Cheng; Kalisch, Henrik (Peer reviewed; Journal article, 2016-04)
      Watershed segmentation is useful for a number of image segmentation problems with a wide range of practical applications. Traditionally, the tracking of the immersion front is done by applying a fast sorting algorithm. In ...
    • The Whitham Equation as a model for surface water waves 

      Moldabayev, Daulet; Kalisch, Henrik; Dutykh, Denys (Peer reviewed; Journal article, 2015-08)
      The Whitham equation was proposed as an alternate model equation for the simplified description of uni-directional wave motion at the surface of an inviscid fluid. As the Whitham equation incorporates the full linear ...