The KP equation with quasiperiodic initial data
نویسنده
چکیده
The Kadomtsev-Petviashvili (KP) equation is known to admit exact, quasiperiodic solutions that can be written in terms of Riemann theta functions, with a nite number of phases in each solution. In this paper, we propose a method to solve the initial-value problem for the KP equation, for initial data taken from this class of quasiperiodic functions.
منابع مشابه
Canonical Variables for multiphase solutions of the KP equation
The KP equation has a large family of quasiperiodic multiphase solutions. These solutions can be expressed in terms of Riemann-theta functions. In this paper, a finite-dimensional canonical Hamiltonian system depending on a finite number of parameters is given for the description of each such solution. The Hamiltonian systems are completely integrable in the sense of Liouville. In effect, this ...
متن کاملOn Analytic Families of Invariant Tori for Pdes
Abstract. — We propose to apply a version of the classical Stokes expansion method to the perturbative construction of invariant tori for PDEs corresponding to solutions quasiperiodic in space and time variables. We argue that, for integrable PDEs all but finite number of the small divisors arising in the perturbative analysis cancel. As an illustrative example we establish such cancellations f...
متن کاملDislocation Dynamics in a Dodecagonal Quasiperiodic Structure
We have developed a set of numerical tools for the quantitative analysis of defect dynamics in quasiperiodic structures. We have applied these tools to study dislocation motion in the dynamical equation of Lifshitz and Petrich [Phys. Rev. Lett. 79 (1997) 1261] whose steady state solutions include a quasiperiodic structure with dodecagonal symmetry. Arbitrary dislocations, parameterized by the h...
متن کاملNoncommutative Space and the Low–energy Physics of Quasicrystals
We prove that the effective low–energy, nonlinear Schroedinger equation for a particle in the presence of a quasiperiodic potential is the potential–free, nonlinear Schroedinger equation on noncommutative space. Thus quasiperiodicity of the potential can be traded for space noncommutativity when describing the envelope wave of the initial quasiperiodic wave.
متن کاملThe Qkp Limit of the Quantum Euler-poisson Equation
In this paper, we consider the derivation of the Kadomtsev-Petviashvili (KP) equation for cold ion-acoustic wave in the long wavelength limit of the two-dimensional quantum Euler-Poisson system, under different scalings for varying directions in the Gardner-Morikawa transform. It is shown that the types of the KP equation depend on the scaled quantum parameter H > 0. The QKP-I is derived for H ...
متن کامل