Periodic solutions to weakly nonlinear autonomous wave equations
نویسندگان
چکیده
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 کاملPeriodic Solutions of Nonlinear Wave Equations
where f is a given continuous function in R 3 and f is T-periodic in t and s. Periodic solutions of nonlinear hyperbolic partial differential equations have been studied extensively in the recent years [1, 6, 7, 8, 9, 10, 11, 12, 13, 14]. The two approaches that have been used are: (i) reduction to an alternative problem and (ii) the Galerkin method and passage to the limit through a sequence o...
متن کاملExact Periodic Wave Solutions to Some Nonlinear Evolution Equations
In this paper, the extended mapping method with symbolic computation is developed to obtain exact periodic wave solutions for nonlinear evolution equations arising in mathematical 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 differential equations, as long as...
متن کاملSolitons and Periodic Wave Solutions for Coupled Nonlinear Equations
In this work we apply the tanh-coth method and the tan-cot method to study some nonlinear coupled equations. Four nonlinear coupled equations that appear in a variety of scientific applications are investigated. We derive soliton, singular solitons and periodic wave solutions for these coupled equations. The obtained results show that these four coupled equations reveal richness of explicit sol...
متن کاملPeriodic solutions for completely resonant nonlinear wave equations
We consider the nonlinear string equation with Dirichlet boundary conditions uxx−utt = φ(u), with φ(u) = Φu+O(u) odd and analytic, Φ 6= 0, and we construct small amplitude periodic solutions with frequency ω for a large Lebesgue measure set of ω close to 1. This extends previous results where only a zero-measure set of frequencies could be treated (the ones for which no small divisors appear). ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1975
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1975.101350