On the Nature of Initial-Boundary Value Solutions for Dispersive Equations
Copyright policy )On the Nature of Initial-Boundary Value Solutions for Dispersive Equations
Summary: If the initial and boundary data for a partial differential equation (PDE) do not obey an infinite set of compatibility conditions, singularities will arise in its solutions. For dissipative equations, these singularities are well localized in both time and space, and an effective numerical remedy is available for accurate computation of initial transients. This study analyzes the nature of similar corner discrepancies for dispersive equations, such as \(u_{t}-u_{xxx}=0\) and \(iu_{t}-u_{xx}=0\).
linear Schrödinger equation, Smoothness and regularity of solutions to PDEs, corner singularities, IBV solutions, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Singularity in context of PDEs, Boundary value problems for linear higher-order PDEs, dispersive equations, corner basis functions, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, compatibility conditions, linearized KdV equation
linear Schrödinger equation, Smoothness and regularity of solutions to PDEs, corner singularities, IBV solutions, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Singularity in context of PDEs, Boundary value problems for linear higher-order PDEs, dispersive equations, corner basis functions, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, compatibility conditions, linearized KdV equation
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