Extremal periodic wave profiles
نویسنده
چکیده
As a contribution to deterministic investigations into extreme fluid surface waves, in this paper wave profiles of prescribed period that have maximal crest height will be investigated. As constraints the values of the momentum and energy integrals are used in a simplified description with the KdV model. The result is that at the boundary of the feasible region in the momentum-energy plane, the only possible profiles are the well known cnoidal wave profiles. Inside the feasible region the extremal profiles of maximal crest height are “cornered” cnoidal profiles: cnoidal profiles of larger period, cut-off and periodically continued with the prescribed period so that at the maximal crest height a corner results.
منابع مشابه
Periodic Wave Shock solutions of Burgers equations
In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...
متن کاملAnalytical Analysis of The Dual-phase-lag Heat Transfer Equation in a Finite Slab with Periodic Surface Heat Flux (RESEARCH NOTE)
This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the ...
متن کاملDevelopment of Forward-wave Directional Couplers Loaded by Periodic Shunt Shorted Stubs
In this paper a new procedure for designing forward-wave directional couplers using periodic shunt short circuited stubs is proposed. A new type of cell using these stubs, which enlarge the phase difference between even- and odd modes of a uniform microstrip coupled line is introduced. Using the equivalent circuit model for even- and odd-modes of the proposed cell, the elements of the ABCD tra...
متن کاملThe Extremal Index of Sub-sampled Periodic Sequences with Strong Local Dependence
• Let X = {Xn}n≥1 be a T -periodic sequence. We define a family of local dependence conditions D (k) T (u), k ≥ 1, and calculate the extremal index θX from the distributions of k consecutive variables of X. For a periodic sub-sampled sequence Y = {Xg(n)}n≥1, where g generates blocks of I1 observations separated by J observations, we present results on local and long range dependence conditions ...
متن کاملExtremal Values of Half-Eigenvalues for p-Laplacian with Weights in L1 Balls
For one-dimensional p-Laplacian with weights in Lγ : L 0, 1 ,R 1 ≤ γ ≤ ∞ balls, we are interested in the extremal values of the mth positive half-eigenvalues associated with Dirichlet, Neumann, and generalized periodic boundary conditions, respectively. It will be shown that the extremal value problems for half-eigenvalues are equivalent to those for eigenvalues, and all these extremal values a...
متن کامل