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Saturday, October 17, 2020 | History

2 edition of **Virial relations for nonlinear wave equations and nonexistence of almost periodic solutions** found in the catalog.

Virial relations for nonlinear wave equations and nonexistence of almost periodic solutions

Randall Mitchell Pyke

- 340 Want to read
- 16 Currently reading

Published
**1996**
by Dept. of Mathematics, University of Toronto in Toronto
.

Written in English

**Edition Notes**

Statement | Randall Pyke. |

Series | Preprint / University of Toronto, Dept. of Mathematics |

The Physical Object | |
---|---|

Pagination | 53 leaves. |

Number of Pages | 53 |

ID Numbers | |

Open Library | OL15447819M |

We construct time quasi-periodic solutions to nonlinear wave equations on the torus in arbitrary dimensions. All previously known results (in the case of zero or a multiplicative potential) seem to be limited to the circle. This extends the method developed in the limit-elliptic setting in to the hyperbolic setting. The additional ingredient is. EXAMPLE SHEET 1: NONLINEAR WAVE EQUATIONS 3 (10) Consider the linear wave equation in R R3. First, show that spherically symmetric (smooth, compactly supported) data lead to spherically symmetric solutions. Moreover, the wave equation becomes @ [email protected] v(r˚) = 0. Then, use this to construct solutions such that (sup x j˚j)(t) C 1 + t for some C>0.

Now if ϕ 1 and ϕ 2 are two solutions of this family, a 1 ϕ 1 and a 2 ϕ 2 are also solutions of the nonlinear wave equation, since it is both homogeneous and invariant under the chiral gauge. But the sum a 1 ϕ 1 + a 2 ϕ 2 is not able to be a solution of the nonlinear wave equation because the determinant giving the Yvon-Takabayasi angle is. nonlinear wave equations and reaction–diffusion equations with several nonlinear source terms of different signs at high energy level - volume 54 issue 3 - runzhang xu, yanbing yang, shaohua chen, jia su, jihong shen, shaobin huang.

Hydrodynamic dispersion in porous media with macroscopic disorder of parameters. NASA Astrophysics Data System (ADS) Goldobin, D. S.; Maryshev, B. S. We present an ana. Periodic Solutions of Nonlinear Wave Equations L. CESARI & R. KANNAN 1. Introduction In this paper we obtain sufficient conditions for the existence of doubly periodic solutions of the nonlinear wave equation ut~ -~ f(t, s, u), (1) u(t + T, s) = u(t, s) = u(t, s + T), (2) where f is a given continuous function in R 3 and f is T-periodic in t.

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In this paper, we prove several nonexistence and existence results for certain real solutions to semilinear wave equations in one space dimension. These solutions represent time almost-periodic. Virial Relations for Nonlinear Wave Equations and Nonexistence of almost Periodic Solutions - NASA/ADS We present a formalism for constructing integral identities involving time almost periodic solutions of nonlinear wave equations.

As an application we prove a nonexistence theorem that is applicable to a large class of nonlinearities.

P />Cited by: 2. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We present a formalism for constructing integral identities involving time almostperiodic solutions of nonlinear wave equations.

As an application we prove a nonexistence theorem that is applicable to a large class of nonlinearities. Virial Relations for Nonlinear Wave Equations and Nonexistence of Almost-Periodic Solutions.

By Randall Pyke. Abstract. We present a formalism for constructing integral identities involving time almostperiodic solutions of nonlinear wave equations. As an application we prove a nonexistence theorem that is applicable to a large class of Author: Randall Pyke.

Stability of Periodic or Almost Periodic Solutions. Alain Haraux book gathers the revised lecture notes from a seminar course offered at the Federal University of Rio de Janeiro inthen in Tokyo in An additional chapter has been added to reflect more recent advances in the field.

Keywords. Wave equation Nonlinear vibrations. Song Y, Tian H: Periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay.

Journal of Computational and Applied Mathematics(2) / MATH MathSciNet Article Google Scholar. The book offers a collection of original papers and expository articles mainly devoted to the study of nonlinear wave equations.

The articles cover a wide range of topics, including scattering theory, dispersive waves, classical field theory, mathematical fluid dynamics, kinetic theory, stability theory, and variational methods. periodic wave solutions of a special-type of nonlinear equations. The aim of this paper is to present the mixed dn-sn method and use it to obtain various periodic wave solutions of some nonlinear wave equations.

This paper is organizedas follows. In Sect. 2 we de-scribe the mixed dn-sn method to construct multiple periodic wave solutions of. [1] B. Bilgin and V. Kalantarov, Blow up of solutions to the initial boundary value problem for quasilinear strongly damped wave equations, J.

Math. Anal. Appl., (), doi: / Google Scholar [2] L. Bociu and I. Lasiecka, Local Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping, J.

Differential Equations. for n>1 too, there is a dispersion relation associated to any linear wave equation, and the Fourier magic still works; i.e., for each ξ there will be a unique frequency ω (ξ) such that u. We present a formalism for constructing integral identities involving time almost periodic solutions of nonlinear wave equations.

As an application we prove a nonexistence theorem that is applicable to a large class of nonlinearities. From planar solutions of Novikov–Veselov to KdV 73 86; 3. A Pseudo-Spectral method for the solution of (2+1) nonlinear wave equations 75 88; 4.

Instability of traveling-wave solutions of the NV-equation to transverse perturbations 79 92; 5. Numerical Results on the Instabilities of Plane-Wave Soliton Solutions 84 97; 6. Conclusions 87 be applied to other nonlinear wave equations: as a warm-up we construct periodic solutions of a boundary-value problem for a large class of nonlinear scalar wave equations.

The argument is inspired by a method introduced in [8], where families of complex valued tensor elds were used to construct stationary black hole solutions of the Einstein.

(subscripts denote partial derivatives). This is the wave equation in one (spatial) dimension. The assumption that one can add the waves together agrees with the linearity of the wave equation; any linear combination of solutions of () is also a solution of ().

A better way of deriving the wave equation is to start from physical principles. The closed form solutions are given by wa y of example only, as nonlinear wave equations often have man y possible solutions.

Revised: J 9 Linear and Nonlinear wav es. article we present new nonexistence results using virial relations and the almost periodicity of (the candidate) bound state solutions.

2 Statement of Results To state our main result we introduce some notation and deﬁnitions. Both NLW and NLS can be written as evolution equations; ∂ tϕ = Aϕ+G(ϕ), () where in the case of NLW, A = 0 1 ∆ 0.

Contents Introduction 1 1 Exponential Bounds and Constraints on Frequencies 3 I.1 Introduction. Equation () is a simple example of wave equation; it may be used as a model of an inﬁnite elastic string, propagation of sound waves in a linear medium, among other numerous applications.

We shall discuss the basic properties of solutions to the wave equation (), as well as its multidimensional and non-linear variants.

Cite this paper as: Strauss W.A. () Nonlinear invariant wave equations. In: Velo G., Wightman A.S. (eds) Invariant Wave Equations. Lecture Notes in Physics, vol We use DDNLW to denote a semi-linear wave equation whose non-linear term is quadratic in the derivatives, i.e. \Box f = G (f) D f D f.

A fairly trivial example of such equations arise by considering fields of the form f = f(u), where f is a given smooth function (e.g. f(x) = exp(ix)) and u is a scalar solution to the free wave equation. EXAMPLE SHEET 2: NONLINEAR WAVE EQUATIONS Throughout this example sheet, we take 2= @ t +.

Notice that the examples with are comparatively advanced. (1) Consider the equation [email protected] t ˚ 2 2 X3 i=1 @ i˚@ 2 ti ˚+ 2 X3 i;j=1 @˚@ j˚@2 ij ˚ X3 i=1 @2 i ˚= 0 in I R3. Given smooth and compactly initial data such that k(˚ 0;˚ 1)k W 1; (R3) L, show.ical physics. Limit cases are studied and new solitary wave solutions and triangular periodic wave solutions are obtained.

The method is applicable to a large variety of nonlinear partial dif-ferential equations, as long as odd and even-order derivative terms do not coexist in the equation .Periodic solutions of a nonlinear wave equation Abbas Bahri and Haim Brezis Analyse Numefique, Universite Paris VI, T 4 pi.

Jussieu, Paris Cedex 05 (MS received 23 May ) SYNOPSIS We provide a sufficient and "almost" necessary condition for the existence of a periodic solution of the equation uB-uxx+F(x,t,u) = 0.