Higher Order Modulation Equations for a Boussinesq Equation
نویسندگان
چکیده
منابع مشابه
Higher Order Modulation Equations for a Boussinesq Equation
In order to investigate corrections to the common KdV approximation to long waves, we derive modulation equations for the evolution of long wavelength initial data for a Boussinesq equation. The equations governing the corrections to the KdV approximation are explicitly solvable and we prove estimates showing that they do indeed give a significantly better approximation than the KdV equation al...
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Zufiria’s higher-order Boussinesq type equations are studied by transforming them into solvable ordinary differential equations. Various families of their travelling wave solutions are generated, which include periodic wave, solitary wave, periodic-like wave, solitonlike wave, Jacobi elliptic function periodic wave, combined non-degenerative Jacobi elliptic function-like wave, Weierstrass ellip...
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1 Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, Maryland 20742. 2 Institute for Scientific Computing and Applied Mathematics and Department of Mathematics, Indiana University, Bloomington, Indiana 47405. E-mail: [email protected] 3 Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109. Received February ...
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Standard perturbation methods are applied to Euler’s equations of motion governing the capillary-gravity shallow water waves to derive a general higher-order Boussinesq equation involving the small-amplitude parameter, α = a/h0, and long-wavelength parameter, β = (h0/l), where a and l are the actual amplitude and wavelength of the surface wave, and h0 is the height of the undisturbed water surf...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Dynamical Systems
سال: 2002
ISSN: 1536-0040
DOI: 10.1137/s1111111102411298