17 Result(s)
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Henrik Kalisch
Mathematics
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Article
Open AccessOn Existence and Admissibility of Singular Solutions for Systems of Conservation Laws
A weak notion of solution for systems of conservation laws in one dimension is put forward. In the framework introduced here, it can be shown that the Cauchy problem for any
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Article
Open AccessA Nonlinear Formulation of Radiation Stress and Applications to Cnoidal Shoaling
In this article, we provide formulations of energy flux and radiation stress consistent with the scaling regime of the Korteweg–de Vries (KdV) equation. These quantities can be used to describe the shoaling of...
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Article
Open AccessWave Breaking in Undular Bores with Shear Flows
It is well known that weak hydraulic jumps and bores develop a growing number of surface oscillations behind the bore front. Defining the bore strength as the ratio of the head of the undular bore to the undis...
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Article
Fully dispersive Boussinesq models with uneven bathymetry
Three weakly nonlinear but fully dispersive Whitham–Boussinesq systems for uneven bathymetry are studied. The derivation and discretization of one system is presented. The numerical solutions of all three are ...
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Article
Special Issue Dedicated to Kristian B. Dysthe
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Article
A Conversation with Kristian Dysthe
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Article
Open AccessParticle Trajectories in Nonlinear Schrödinger Models
The nonlinear Schrödinger equation is well known as a universal equation in the study of wave motion. In the context of wave motion at the free surface of an incompressible fluid, the equation accurately predi...
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Article
Editorial
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Article
Open AccessConvective wave breaking in the KdV equation
The KdV equation is a model equation for waves at the surface of an inviscid incompressible fluid, and it is well known that the equation describes the evolution of unidirectional waves of small amplitude and ...
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Article
Open AccessOn the Formulation of Mass, Momentum and Energy Conservation in the KdV Equation
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 d...
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Article
Preface
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Article
A dispersive model for undular bores
In this article, consideration is given to weak bores in free-surface flows. The energy loss in the shallow-water theory for an undular bore is thought to be due to upstream oscillations that carry away the en...
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Article
Open AccessMechanical Balance Laws for Boussinesq Models of Surface Water Waves
Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features ...
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Chapter and Conference Paper
The Stability of Solitary Waves of Depression
We provide a sufficient condition for the orbital stability of negative solitary-wave solutions of the regularized long-wave equation. In particular, it is found that solitary waves with speed
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Article
Error Analysis of a Spectral Projection of the Regularized Benjamin–Ono Equation
The regularized Benjamin–Ono equation appears in the modeling of long-crested interfacial waves in two-fluid systems. For this equation, Fourier–Galerkin and collocation semi-discretizations are proved to be s...
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Article
Open AccessPeriodic Traveling Water Waves with Isobaric Streamlines
It is shown that in water of finite depth, there are no periodic traveling waves with the property that the pressure in the underlying fluid flow is constant along streamlines. In the case of infinite depth, t...
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Article
Open AccessThe Derivative Nonlinear Schrödinger Equation in Analytic Classes
The derivative nonlinear Schrödinger equation is shown to be locally well-posed in a class of functions analytic on a strip around the real axis. The main feature of the result is that the width of the strip does...
