15,478 research outputs found
Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation
In this paper, we investigate the (2+1) dimensional long wave-short wave
resonance interaction (LSRI) equation and show that it possess the Painlev\'e
property. We then solve the LSRI equation using Painlev\'e truncation approach
through which we are able to construct solution in terms of three arbitrary
functions. Utilizing the arbitrary functions present in the solution, we have
generated a wide class of elliptic function periodic wave solutions and
exponentially localized solutions such as dromions, multidromions, instantons,
multi-instantons and bounded solitary wave solutions.Comment: 13 pages, 6 figure
Coupled KdV equations derived from atmospherical dynamics
Some types of coupled Korteweg de-Vries (KdV) equations are derived from an
atmospheric dynamical system. In the derivation procedure, an unreasonable
-average trick (which is usually adopted in literature) is removed. The
derived models are classified via Painlev\'e test. Three types of
-function solutions and multiple soliton solutions of the models are
explicitly given by means of the exact solutions of the usual KdV equation. It
is also interesting that for a non-Painlev\'e integrable coupled KdV system
there may be multiple soliton solutions.Comment: 19 pages, 2 figure
A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions and its applications
A nonlinear transformation of the dispersive long wave equations in (2+1)
dimensions is derived by using the homogeneous balance method. With the aid of
the transformation given here, exact solutions of the equations are obtained
Periodicities in Solar Coronal Mass Ejections
Mid-term quasi-periodicities in solar coronal mass ejections (CMEs) during
the most recent solar maximum cycle 23 are reported here for the first time
using the four-year data (February 5, 1999 to February 10, 2003) of the Large
Angle Spectrometric Coronagraph (LASCO) onboard the Solar and Heliospheric
Observatory (SOHO). In parallel, mid-term quasi-periodicities in solar X-ray
flares (class >M5.0) from the Geosynchronous Operational Environment Satellites
(GOES) and in daily averages of Ap index for geomagnetic disturbances from the
World Data Center (WDC) at the International Association for Geomagnetism and
Aeronomy (IAGA) are also examined for the same four-year time span. Several
conceptual aspects of possible equatorially trapped Rossby-type waves at and
beneath the solar photosphere are discussed.Comment: Accepted by MNRAS, 6 figure
From one to infinity: symmetries of integrable systems
Integrable systems constitute an essential part of modern physics.
Traditionally, to approve a model is integrable one has to find its infinitely
many symmetries or conserved quantities. In this letter, taking the well known
Korteweg-de Vries and Boussinesq equations as examples, we show that it is
enough to find only one nonlocal key-symmetry to guarantee the integrability.
Starting from the nonlocal key-symmetry, recursion operator(s) and then
infinitely many symmetries and Lax pairs can be successfully found.Comment: 6 page
New variable separation approach: application to nonlinear diffusion equations
The concept of the derivative-dependent functional separable solution, as a
generalization to the functional separable solution, is proposed. As an
application, it is used to discuss the generalized nonlinear diffusion
equations based on the generalized conditional symmetry approach. As a
consequence, a complete list of canonical forms for such equations which admit
the derivative-dependent functional separable solutions is obtained and some
exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig
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