Gauge-invariant description of some (2+1)-dimensional integrable nonlinear evolution equations

نویسندگان

  • V. G. Dubrovsky
  • A. V. Gramolin
چکیده

New manifestly gauge-invariant forms of two-dimensional generalized dispersive long wave and NizhnikVeselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous two-dimensional generalization of dispersive long wave system of equations, Nizhnik-Veselov-Novikov and modified Nizhnik-Veselov-Novikov equations and other known and new integrable nonlinear equations arise. Miura-type transformations between nonlinear equations in different gauges are considered.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations

We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada–Kotera and Kaup–Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik–Veselov–Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada–Kotera equation, Kaup–Kuperschmidt equation, disp...

متن کامل

The Gauge Equivalence of the Zakharov Equations and (2+1)-dimensional Continuous Heisenberg Ferromagnetic Models

The gauge equivalence between the (2+1)-dimensional Zakharov equation and (2+1)-dimensional integrable continuous Heisenberg ferromagnetic model is established. Also their integrable reductions are shown explicitly. Preprint CNLP-1994-04. Alma-Ata.1994 The concepts of gauge equivalence between completely integrable equations plays important role in the theory of solitons[1,2]. In the (2+1)-dime...

متن کامل

New Exact Solutions of Some Two-Dimensional Integrable Nonlinear Equations via ∂-Dressing Method

In the last two decades the Inverse Spectral Transform (IST) method has been generalized and successfully applied to various (2 + 1)-dimensional nonlinear evolution equations such as Kadomtsev–Petviashvili, Davey–Stewardson, Nizhnik–Veselov–Novikov, Zakharov–Manakov system, Ishimory, two dimensional integrable sine-Gordon and others (see books [1, 2, 3, 4] and references therein). The nonlocal ...

متن کامل

New explicit and Soliton Wave Solutions of Some Nonlinear Partial Differential Equations with Infinite Series Method

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...

متن کامل

Integrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials

Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008