Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations
نویسندگان
چکیده
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, dispersive long-wave system, Nizhnik–Veselov–Novikov equation, and modified Nizhnik–Veselov– Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges.
منابع مشابه
Gauge-invariant description of some (2+1)-dimensional integrable nonlinear evolution equations
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 an...
متن کاملThe 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 کاملGauge Transformations and Weak Lax Equation
We consider several integrable systems from a standpoint of the SL(2,R) invariant gauge theory. In the Drinfeld-Sokorov gauge, we get a one parameter family of nonlinear equations from zero curvature conditions. For each value of the parameter the equation is described by weak Lax equations. It is transformed to a set of coupled equations which pass the Painlevé test and are integrable for any ...
متن کاملNew 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 کاملSolutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation
Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Ri...
متن کامل